1
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Maire R, Plati A. Enhancing (quasi-)long-range order in a two-dimensional driven crystal. J Chem Phys 2024; 161:054902. [PMID: 39087549 DOI: 10.1063/5.0217958] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2024] [Accepted: 07/14/2024] [Indexed: 08/02/2024] Open
Abstract
It has been recently shown that 2D systems can exhibit crystalline phases with long-range translational order showcasing a striking violation of the Hohenberg-Mermin-Wagner (HMW) theorem, which is valid at equilibrium. This is made possible by athermal driving mechanisms that inject energy into the system without exciting long wavelength modes of the density field, thereby inducing hyperuniformity. However, as thermal fluctuations are superimposed on the non-equilibrium driving, long-range translational order is inevitably lost. Here, we discuss the possibility of exploiting non-equilibrium effects to suppress arbitrarily large density fluctuations even when a global thermal bath is coupled to the system. We introduce a model of a harmonic crystal driven both by a global thermal bath and by a momentum conserving noise, where the typical observables related to density fluctuations and long-range translational order can be analytically derived and put in relation. This model allows us to rationalize the violation of the HMW theorem observed in previous studies through the prediction of large-wavelength phonons, which thermalize at a vanishing effective temperature when the global bath is switched off. The conceptual framework introduced through this theory is then applied to numerical simulations of a hard-disk solid in contact with a thermal bath and driven out-of-equilibrium by active collisions. Our numerical analysis demonstrates how varying driving and dissipative parameters can lead to an arbitrary enhancement of the quasi-long-range order in the system regardless of the applied global noise amplitude. Finally, we outline a possible experimental procedure to apply our results to a realistic granular system.
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Affiliation(s)
- R Maire
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - A Plati
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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2
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Fernandez L, Hess S, Klapp SHL. Nonequilibrium dynamics and entropy production of a trapped colloidal particle in a complex nonreciprocal medium. Phys Rev E 2024; 109:054129. [PMID: 38907489 DOI: 10.1103/physreve.109.054129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Accepted: 05/02/2024] [Indexed: 06/24/2024]
Abstract
We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modeled by a linear, typically nonreciprocal coupling of the particle coordinates to an auxiliary (hidden) variable. The system's behavior resulting from the microscopic Langevin equations for the three variables is analyzed by means of exact moment equations derived from the Fokker-Planck representation, and numerical Brownian dynamics simulations. Increasing the shear rate beyond a critical value we observe, for suitable coupling scenarios with nonreciprocal elements, a transition from a stationary to a nonstationary state, corresponding to an escape from the trap. We analyze this behavior, analytically and numerically, in terms of the associated moments of the probability distribution, and from the perspective of nonequilibrium thermodynamics. Intriguingly, the entropy production rate remains finite when crossing the stability threshold.
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3
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Viot P, Argun A, Volpe G, Imparato A, Rondoni L, Oshanin G. Destructive effect of fluctuations on the performance of a Brownian gyrator. SOFT MATTER 2024; 20:3154-3160. [PMID: 38512337 DOI: 10.1039/d3sm01606d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/22/2024]
Abstract
The Brownian gyrator (BG) is often called a minimal model of a nano-engine performing a rotational motion, judging solely upon the fact that in non-equilibrium conditions its torque, specific angular momentum and specific angular velocity have non-zero mean values. For a time-discretised (with time-step δt) model we calculate here the previously unknown probability density functions (PDFs) of and . We show that for finite δt, the PDF of has exponential tails and all moments are therefore well-defined. At the same time, this PDF appears to be effectively broad - the noise-to-signal ratio is generically bigger than unity meaning that is strongly not self-averaging. Concurrently, the PDF of exhibits heavy power-law tails and its mean is the only existing moment. The BG is therefore not an engine in the common sense: it does not exhibit regular rotations on each run and its fluctuations are not only a minor nuisance - on contrary, their effect is completely destructive for the performance. Our theoretical predictions are confirmed by numerical simulations and experimental data. We discuss some plausible improvements of the model which may result in a more systematic rotational motion.
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Affiliation(s)
- Pascal Viot
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 Place Jussieu, Paris 75252, Cedex 05, France.
| | - Aykut Argun
- Physics Department, University of Gothenburg, Gothenburg 412 96, Sweden
| | - Giovanni Volpe
- Physics Department, University of Gothenburg, Gothenburg 412 96, Sweden
| | - Alberto Imparato
- Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, Building 1520, Aarhus C DK-8000, Denmark
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy
- INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 Place Jussieu, Paris 75252, Cedex 05, France.
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4
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Ohga N, Ito S, Kolchinsky A. Thermodynamic Bound on the Asymmetry of Cross-Correlations. PHYSICAL REVIEW LETTERS 2023; 131:077101. [PMID: 37656850 DOI: 10.1103/physrevlett.131.077101] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 06/08/2023] [Indexed: 09/03/2023]
Abstract
The principle of microscopic reversibility says that, in equilibrium, two-time cross-correlations are symmetric under the exchange of observables. Thus, the asymmetry of cross-correlations is a fundamental, measurable, and often-used statistical signature of deviation from equilibrium. Here we find a simple and universal inequality that bounds the magnitude of asymmetry by the cycle affinity, i.e., the strength of thermodynamic driving. Our result applies to a large class of systems and all state observables, and it suggests a fundamental thermodynamic cost for various nonequilibrium functions quantified by the asymmetry. It also provides a powerful tool to infer affinity from measured cross-correlations, in a different and complementary way to the thermodynamic uncertainty relations. As an application, we prove a thermodynamic bound on the coherence of noisy oscillations, which was previously conjectured by Barato and Seifert [Phys. Rev. E 95, 062409 (2017)PRESCM2470-004510.1103/PhysRevE.95.062409]. We also derive a thermodynamic bound on directed information flow in a biochemical signal transduction model.
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Affiliation(s)
- Naruo Ohga
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Sosuke Ito
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Artemy Kolchinsky
- Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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5
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Caprini L, Marini Bettolo Marconi U, Puglisi A, Löwen H. Entropons as collective excitations in active solids. J Chem Phys 2023; 159:041102. [PMID: 37486049 DOI: 10.1063/5.0156312] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 07/05/2023] [Indexed: 07/25/2023] Open
Abstract
The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers.
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Affiliation(s)
- Lorenzo Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi-CNR and Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
- INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Hartmut Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
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6
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Nandi MK, de Candia A, Sarracino A, Herrmann HJ, de Arcangelis L. Fluctuation-dissipation relations in the imbalanced Wilson-Cowan model. Phys Rev E 2023; 107:064307. [PMID: 37464662 DOI: 10.1103/physreve.107.064307] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 05/15/2023] [Indexed: 07/20/2023]
Abstract
The relation between spontaneous and stimulated brain activity is a fundamental question in neuroscience which has received wide attention in experimental studies. Recently, it has been suggested that the evoked response to external stimuli can be predicted from temporal correlations of spontaneous activity. Previous theoretical results, confirmed by the comparison with magnetoencephalography data for human brains, were obtained for the Wilson-Cowan model in the condition of balance of excitation and inhibition, a signature of a healthy brain. Here we extend previous studies to imbalanced conditions by examining a region of parameter space around the balanced fixed point. Analytical results are compared to numerical simulations of Wilson-Cowan networks. We evidence that in imbalanced conditions the functional form of the time correlation and response functions can show several behaviors, exhibiting also an oscillating regime caused by the emergence of complex eigenvalues. The analytical predictions are fully in agreement with numerical simulations, validating the role of cross-correlations in the response function. Furthermore, we identify the leading role of inhibitory neurons in controlling the overall activity of the system, tuning the level of excitability and imbalance.
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Affiliation(s)
- Manoj Kumar Nandi
- Department of Engineering, University of Campania "Luigi Vanvitelli" 81031 Aversa (Caserta), Italy
| | - Antonio de Candia
- Department of Physics "E. Pancini", University of Naples Federeico II, 80126 Naples, Italy
- INFN, Section of Naples, Gruppo collegato di Salerno, 84084 Fisciano, Italy
| | - Alessandro Sarracino
- Department of Engineering, University of Campania "Luigi Vanvitelli" 81031 Aversa (Caserta), Italy
- Institute for Complex Systems-CNR, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Hans J Herrmann
- PMMH, ESPCI, 7 quai St. Bernard, Paris 75005, France
- Department of Physics, Federal University of Ceará, Fortaleza, Ceará 60451-970, Brazil
| | - Lucilla de Arcangelis
- Department of Mathematics & Physics, University of Campania "Luigi Vanvitelli" Viale Lincoln, 5, 81100 Caserta, Italy
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7
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Plati A, Puglisi A, Sarracino A. Thermodynamic bounds for diffusion in nonequilibrium systems with multiple timescales. Phys Rev E 2023; 107:044132. [PMID: 37198828 DOI: 10.1103/physreve.107.044132] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Accepted: 03/21/2023] [Indexed: 05/19/2023]
Abstract
We derive a thermodynamic uncertainty relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to previous results and also holds at finite time. We apply our findings to experimental and numerical data for a vibrofluidized granular medium, characterized by regimes of anomalous diffusion. In some cases our relation can distinguish between equilibrium and nonequilibrium behavior, a nontrivial inference task, particularly for Gaussian processes.
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Affiliation(s)
- A Plati
- Department of Physics, University of Rome Sapienza, Piazzale Aldo Moro 2, 00185, Rome, Italy
- Institute for Complex Systems-CNR, Piazzale Aldo Moro 2, 00185, Rome, Italy
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - A Puglisi
- Department of Physics, University of Rome Sapienza, Piazzale Aldo Moro 2, 00185, Rome, Italy
- Institute for Complex Systems-CNR, Piazzale Aldo Moro 2, 00185, Rome, Italy
- INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy
| | - A Sarracino
- Institute for Complex Systems-CNR, Piazzale Aldo Moro 2, 00185, Rome, Italy
- Department of Engineering, University of Campania "Luigi Vanvitelli," 81031 Aversa (CE), Italy
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8
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Crisanti A, Paoluzzi M. Most probable path of active Ornstein-Uhlenbeck particles. Phys Rev E 2023; 107:034110. [PMID: 37072947 DOI: 10.1103/physreve.107.034110] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
Using the path integral representation of the nonequilibrium dynamics, we compute the most probable path between arbitrary starting and final points that is followed by an active particle driven by persistent noise. We focus our attention on the case of active particles immersed in harmonic potentials, where the trajectory can be computed analytically. Once we consider the extended Markovian dynamics where the self-propulsive drive evolves according to an Ornstein-Uhlenbeck process, we can compute the trajectory analytically with arbitrary conditions on position and self-propulsion velocity. We test the analytical predictions against numerical simulations and we compare the analytical results with those obtained within approximated equilibriumlike dynamics.
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Affiliation(s)
- Andrea Crisanti
- Dipartimento di Fisica, Sapienza Università di Roma Piazzale A. Moro 2, I-00185 Rome, Italy
| | - Matteo Paoluzzi
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, C. Martí Franquès 1, 08028 Barcelona, Spain
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9
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Gaindrik P, Baul U, Dzubiella J. Active responsive colloids coupled to different thermostats. Phys Rev E 2022; 106:014613. [PMID: 35974513 DOI: 10.1103/physreve.106.014613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Accepted: 07/12/2022] [Indexed: 06/15/2023]
Abstract
We introduce a model of active responsive colloids (ARCs) in which an internal degree of freedom (DoF) of a single colloidal particle is "activated" by coupling it to a different thermostat than for the translational DoFs. As for the responsive internal DoF, we consider specifically the size (diameter) of the spherical particles, which is confined by a harmonic parent potential being either entropic or energetic in nature. The ARCs interact via a repulsive Hertzian pair potential, appropriate to model hydrogels or elastic colloids, and are studied for various densities using Brownian dynamics simulations. We tune the internal activity in the nonequilibrium steady state by scanning through a wide range of internal temperatures, both smaller ("colder") and larger ("hotter") than the translational temperature. The results show a rich and intriguing behavior for the emergent property distributions, colloidal pair structure, and the diffusive translational dynamics controlled by the internal activity, substantially depending on whether the internal DoF moves in an entropic or energetic potential. We discuss theoretical thermal limits and phenomenological models which can explain some of the nonequilibrium trends qualitatively. Our study indicates that particle dynamical polydispersity as well as the structure and dynamics of dense macromolecular suspensions can be vastly tuned by internal activity in terms of internal "hot" or "cold" fluctuating states.
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Affiliation(s)
- Polina Gaindrik
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
| | - Upayan Baul
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
| | - Joachim Dzubiella
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
- Cluster of Excellence livMatS @ FIT-Freiburg Center for Interactive Materials and Bioinspired Technologies, Albert-Ludwigs-Universität Freiburg, D-79110 Freiburg, Germany
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10
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Cerasoli S, Ciliberto S, Marinari E, Oshanin G, Peliti L, Rondoni L. Spectral fingerprints of nonequilibrium dynamics: The case of a Brownian gyrator. Phys Rev E 2022; 106:014137. [PMID: 35974646 DOI: 10.1103/physreve.106.014137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally relevant model of such a system-the so-called Brownian gyrator-a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under nonequilibrium conditions, while no net rotation takes place under equilibrium ones. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in nonequilibrium. We show that indeed one can conclusively distinguish between equilibrium and nonequilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a nonequilibrium dynamics.
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Affiliation(s)
- Sara Cerasoli
- Department of Civil and Environmental Engineering, Princeton University, Princeton New Jersey 08544, USA
| | - Sergio Ciliberto
- Laboratoire de Physique (UMR CNRS 567246), Ecole Normale Supérieure, Allée d'Italie, 69364 Lyon, France
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma 1 and Nanotech-CNR, UOS di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Luca Peliti
- Santa Marinella Research Institute, Santa Marinella, Italy
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
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11
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Wang M, Zinga K, Zidovska A, Grosberg AY. Tethered tracer in a mixture of hot and cold Brownian particles: can activity pacify fluctuations? SOFT MATTER 2021; 17:9528-9539. [PMID: 34617946 DOI: 10.1039/d1sm01163d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We study how an interacting mixture of components with differing levels of activity can affect the fluctuations of an embedded object such as a tracer. In particular, we consider a simple model of a tracer that is harmonically bound within a mixture of hot and cold Brownian particles, which, like a mixture of active and passive particles, can phase separate. By measuring the fluctuations of the tracer, we find that this collective behavior gives rise to an effective temperature for the tracer. Additionally, we find that there is an increased tendency for cold particles to accumulate on the surface of the tracer due to the hot particles, potentially dampening its fluctuations and decreasing its effective temperature. These results suggest that the phase separation of a mixture of hot/cold or active/passive particles may have strong effects on the fluctuations of an embedded object. We discuss potential implications of these results for experiments on fluctuations of nuclear envelope affected by the activity in the chromatin.
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Affiliation(s)
- Michael Wang
- Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, NY 10003, USA.
| | - Ketsia Zinga
- Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, NY 10003, USA.
| | - Alexandra Zidovska
- Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, NY 10003, USA.
| | - Alexander Y Grosberg
- Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, NY 10003, USA.
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12
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Sarra C, Baldovin M, Vulpiani A. Response and flux of information in extended nonequilibrium dynamics. Phys Rev E 2021; 104:024116. [PMID: 34525640 DOI: 10.1103/physreve.104.024116] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 07/26/2021] [Indexed: 11/07/2022]
Abstract
It is well known that entropy production is a proxy to the detection of nonequilibrium, i.e., of the absence of detailed balance; however, due to the global character of this quantity, its knowledge does not allow to identify spatial currents or fluxes of information among specific elements of the system under study. In this respect, much more insight can be gained by studying transfer entropy and response, which allow quantifying the relative influence of parts of the system and the asymmetry of the fluxes. In order to understand the relation between the above-mentioned quantities, we investigate spatially asymmetric extended systems. First, we consider a simplified linear stochastic model, which can be studied analytically; then, we include nonlinear terms in the dynamics. Extensive numerical investigation shows the relation between entropy production and the above-introduced degrees of asymmetry. Finally, we apply our approach to the highly nontrivial dynamics generated by the Lorenz 96 model for Earth oceanic circulation.
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Affiliation(s)
- Camilla Sarra
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Marco Baldovin
- Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 5, 00185 Rome, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 5, 00185 Rome, Italy
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13
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Bilotto P, Caprini L, Vulpiani A. Excess and loss of entropy production for different levels of coarse graining. Phys Rev E 2021; 104:024140. [PMID: 34525579 DOI: 10.1103/physreve.104.024140] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2021] [Accepted: 08/10/2021] [Indexed: 06/13/2023]
Abstract
We investigate the effect of coarse graining on the thermodynamic properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a sinusoidal potential and driven out of equilibrium by a small constant force. Different levels of coarse graining are evaluated: At first, we compare the results in the underdamped dynamics with those in the overdamped one (first coarse graining). For large values of the friction coefficient, the two dynamics have the same thermodynamics properties, while, for smaller friction values, the overdamped approximation produces an excess of entropy production with respect to that of the underdamped dynamics. Moreover, for further smaller values of the drag coefficient, the excess of entropy production turns into a loss. These regimes are explained by evaluating the jump statistics, observing that the inertia is able to induce multiple jumps and affect the average jump rate. The periodic shape of the potential allows us to approximate the continuous dynamics via a Markov chain after the introduction of a suitable time and space discretization (second level of coarse graining). This discretization procedure is implemented starting both from the underdamped and the overdamped evolution and is analyzed for different values of the friction coefficient.
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Affiliation(s)
- Pierpaolo Bilotto
- Dipartimento di Fisica, Universitá di Roma Sapienza, 00185 Rome, Italy
| | - Lorenzo Caprini
- Scuola di Scienze e Tecnologie, Universitá di Camerino, 62032 Camerino, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica, Universitá di Roma Sapienza, 00185 Rome, Italy
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14
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Wu W, Wang J. Landscape-Flux Framework for Nonequilibrium Dynamics and Thermodynamics of Open Hamiltonian Systems Coupled to Multiple Heat Baths. J Phys Chem B 2021; 125:7809-7827. [PMID: 34232645 DOI: 10.1021/acs.jpcb.1c02261] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We establish a nonequilibrium dynamic and thermodynamic formalism in the landscape-flux framework for open Hamiltonian systems in contact with multiple heat baths governed by stochastic dynamics. To systematically characterize nonequilibrium steady states, the nonequilibrium trinity construct is developed, which consists of detailed balance breaking, nonequilibrium potential landscape, and irreversible probability flux. We demonstrate that the temperature difference of the heat baths is the physical origin of detailed balance breaking, which generates the nonequilibrium potential landscape characterizing the nonequilibrium statistics and creates the irreversible probability flux signifying time irreversibility, with the latter two aspects closely connected. It is shown that the stochastic dynamics of the system can be formulated in the landscape-flux form, where the reversible force drives the conservative Hamiltonian dynamics, the irreversible force consisting of a landscape gradient force and an irreversible flux force drives the dissipative dynamics, and the stochastic force adds random fluctuations to the dynamics. The possible connection of the nonequilibrium trinity construct to nonequilibrium phase transitions is also suggested. A set of nonequilibrium thermodynamic equations, applicable to both nonequilibrium steady states and transient relaxation processes, is constructed. We find that an additional thermodynamic quantity, named the mixing entropy production rate, enters the nonequilibrium thermodynamic equations. It arises from the interplay between detailed balance breaking and transient relaxation, and it also relies on the conservative dynamics. At the nonequilibrium steady state, the heat flow, entropy flow, and entropy production are demonstrated to be thermodynamic manifestations of the nonequilibrium trinity construct. The general nonequilibrium formalism is applied to a class of solvable systems consisting of coupled harmonic oscillators. A more specific example of two harmonic oscillators coupled to two heat baths is worked out in detail. The example may facilitate connection with experiments.
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Affiliation(s)
- Wei Wu
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
| | - Jin Wang
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States.,Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11790, United States
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15
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Jung G, Schmid F. Fluctuation-dissipation relations far from equilibrium: a case study. SOFT MATTER 2021; 17:6413-6425. [PMID: 34132298 PMCID: PMC8262459 DOI: 10.1039/d1sm00521a] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 06/06/2021] [Indexed: 06/12/2023]
Abstract
Fluctuation-dissipation relations or "theorems" (FDTs) are fundamental for statistical physics and can be rigorously derived for equilibrium systems. Their applicability to non-equilibrium systems is, however, debated. Here, we simulate an active microrheology experiment, in which a spherical colloid is pulled with a constant external force through a fluid, creating near-equilibrium and far-from-equilibrium systems. We characterize the structural and dynamical properties of these systems, and reconstruct an effective generalized Langevin equation (GLE) for the colloid dynamics. Specifically, we test the validity of two FDTs: The first FDT relates the non-equilibrium response of a system to equilibrium correlation functions, and the second FDT relates the memory friction kernel in the GLE to the stochastic force. We find that the validity of the first FDT depends strongly on the strength of the external driving: it is fulfilled close to equilibrium and breaks down far from it. In contrast, we observe that the second FDT is always fulfilled. We provide a mathematical argument why this generally holds for memory kernels reconstructed from a deterministic Volterra equation for correlation functions, even for non-stationary non-equilibrium systems. Motivated by the Mori-Zwanzig formalism, we therefore suggest to impose an orthogonality constraint on the stochastic force, which is in fact equivalent to the validity of this Volterra equation. Such GLEs automatically satisfy the second FDT and are unique, which is desirable when using GLEs for coarse-grained modeling.
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Affiliation(s)
- Gerhard Jung
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany.
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16
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Loos SAM, Hermann S, Klapp SHL. Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay. ENTROPY (BASEL, SWITZERLAND) 2021; 23:696. [PMID: 34073091 PMCID: PMC8229647 DOI: 10.3390/e23060696] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Revised: 05/20/2021] [Accepted: 05/26/2021] [Indexed: 11/17/2022]
Abstract
Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system's linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback.
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Affiliation(s)
- Sarah A. M. Loos
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany;
- ICTP—The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 15, 04103 Leipzig, Germany
| | - Simon Hermann
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany;
| | - Sabine H. L. Klapp
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany;
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17
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Martins J, Defaveri L, Soares-Pinto DO, Queirós SMD, Morgado WAM. Non-Markovianity, entropy production, and Jarzynski equality. Phys Rev E 2021; 103:022108. [PMID: 33735963 DOI: 10.1103/physreve.103.022108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2020] [Accepted: 01/13/2021] [Indexed: 11/07/2022]
Abstract
We explore the role a non-Markovian memory kernel plays on information exchange and entropy production in the context of a external work protocol. The Jarzynski equality is shown to hold for both the harmonic and the nonharmonic models. We observe the memory function acts as an information pump, recovering part of the information lost to the thermal reservoir as a consequence of the nonequilibrium work protocol. The pumping action occurs for both the harmonic and nonharmonic cases. Unexpectedly, we found that the harmonic model does not produce entropy, regardless of the work protocol. The presence of even a small amount of nonlinearity recovers the more normal entropy producing behavior, for out-of-equilibrium protocols.
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Affiliation(s)
- Jackes Martins
- Departamento de Física, Pontifícia Universidade Católica, 22451-900, Rio de Janeiro, Brazil
| | - Lucianno Defaveri
- Departamento de Física, Pontifícia Universidade Católica, 22451-900, Rio de Janeiro, Brazil
| | - Diogo O Soares-Pinto
- Instituto de Física de São Carlos, Universidade de São Paulo CP 369, 13560-970, São Carlos, São Paulo, Brazil
| | - Sílvio M Duarte Queirós
- Centro Brasileiro de Pesquisas Físicas, Rua Dr Xavier Sigaud, 150, 22290-180 Rio de Janeiro-RJ, Brazil.,National Institute of Science and Technology for Complex Systems.,i3N, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal
| | - Welles A M Morgado
- Departamento de Física, Pontifícia Universidade Católica, 22451-900, Rio de Janeiro, Brazil.,National Institute of Science and Technology for Complex Systems
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18
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Gnesotto FS, Gradziuk G, Ronceray P, Broedersz CP. Learning the non-equilibrium dynamics of Brownian movies. Nat Commun 2020; 11:5378. [PMID: 33097699 PMCID: PMC7585442 DOI: 10.1038/s41467-020-18796-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 09/10/2020] [Indexed: 01/30/2023] Open
Abstract
Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.
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Affiliation(s)
- Federico S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany
| | - Grzegorz Gradziuk
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany
| | - Pierre Ronceray
- Center for the Physics of Biological Function, Princeton University, Princeton, NJ, 08544, USA.
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany.
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam, HV, 1081, The Netherlands.
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19
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Lee JS, Park JM, Park H. Brownian heat engine with active reservoirs. Phys Rev E 2020; 102:032116. [PMID: 33075980 DOI: 10.1103/physreve.102.032116] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 08/18/2020] [Indexed: 11/07/2022]
Abstract
Microorganisms such as bacteria are active matter which consume chemical energy and generate their unique run-and-tumble motion. A swarm of such microorganisms provide a nonequilibrium active environment whose noise characteristics are different from those of thermal equilibrium reservoirs. One important difference is a finite persistence time, which is considerably large compared to that of the equilibrium noise, that is, the active noise is colored. Here we study a mesoscopic energy-harvesting device (engine) with active reservoirs harnessing this noise nature. For an exactly solvable linear model, we show that the performance from the active environment can surpass that from the equilibrium environment. Furthermore, we propose a proper definition of the active-reservoir temperature and show that the engine efficiency can overcome the conventional Carnot bound, thus the power-efficiency trade-off constraint is released. We also show that the efficiency at the maximum power can surpass the Curzon-Ahlborn efficiency. This remarkable enhancement originates from the extra unconventional entropy production beyond the conventional Clausius entropy production, due to the non-Markovian nature of the active reservoirs. Interestingly, the supremacy of the active engine critically depends on the timescale symmetry of two active reservoirs.
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Affiliation(s)
- Jae Sung Lee
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Jong-Min Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunggyu Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
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20
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Teza G, Stella AL. Exact Coarse Graining Preserves Entropy Production out of Equilibrium. PHYSICAL REVIEW LETTERS 2020; 125:110601. [PMID: 32975992 DOI: 10.1103/physrevlett.125.110601] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Revised: 07/13/2020] [Accepted: 08/10/2020] [Indexed: 06/11/2023]
Abstract
The entropy production rate associated with broken time-reversal symmetry provides an essential characterization of nanosystems out of equilibrium, from driven colloidal particles to molecular motors. Limited access to the dynamical states is generally expected to hinder the correct estimation of this observable. Here we show how memoryless jump processes can be coarse grained, exactly preserving its average and fluctuations at stationarity. This supports univocal applicability of fluctuation theorems for entropy and allows inference of the genuine thermodynamics together with inaccessible process details.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel and Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Attilio L Stella
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy and INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
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21
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Lee JS, Park JM, Chun HM, Um J, Park H. Exactly solvable two-terminal heat engine with asymmetric Onsager coefficients: Origin of the power-efficiency bound. Phys Rev E 2020; 101:052132. [PMID: 32575278 DOI: 10.1103/physreve.101.052132] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2020] [Accepted: 04/30/2020] [Indexed: 11/07/2022]
Abstract
An engine producing a finite power at the ideal (Carnot) efficiency is a dream engine which is not prohibited by the thermodynamic second law. Some years ago, a two-terminal heat engine with asymmetric Onsager coefficients in the linear response regime was suggested by Benenti et al. [Phys. Rev. Lett. 106, 230602 (2011)10.1103/PhysRevLett.106.230602], as a prototypical system to make such a dream come true with nondivergent system parameter values. However, such a system has never been realized, in spite of many trials. Here, we introduce an exactly solvable two-terminal Brownian heat engine with the asymmetric Onsager coefficients in the presence of a Lorenz (magnetic) force. Nevertheless, we show that the dream engine regime cannot be accessible, even with the asymmetric Onsager coefficients, due to an instability keeping the engine from reaching its steady state. This is consistent with recent tradeoff relations between the engine power and efficiency, where the (cyclic) steady-state condition is implicitly presumed. We conclude that the inaccessibility to the dream engine originates from the steady-state constraint on the engine.
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Affiliation(s)
- Jae Sung Lee
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Jong-Min Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyun-Myung Chun
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Jaegon Um
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Hyunggyu Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
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22
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Wang M, Grosberg AY. Three-body problem for Langevin dynamics with different temperatures. Phys Rev E 2020; 101:032131. [PMID: 32290012 DOI: 10.1103/physreve.101.032131] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2019] [Accepted: 02/20/2020] [Indexed: 11/07/2022]
Abstract
A mixture of Brownian particles at different temperatures has been a useful model for studying the out-of-equilibrium properties of systems made up of microscopic components with differing levels of activity. This model was previously studied analytically for two-particle interactions in the dilute limit, yielding a Boltzmann-like two-particle distribution with an effective temperature. Like the Newtonian two- and three-body problems, we ask here whether the two-particle results can be extended to three-particle interactions to get the three-particle distributions. By considering the special solvable case of pairwise quadratic interactions, we show that, unlike the two-particle distribution, the three-particle distribution cannot in general be Boltzmann-like with an effective temperature. We instead find that the steady-state distribution of any two particles in a triplet depends on the properties of and interactions with the third particle, leading to some unexpected behaviors not present in equilibrium.
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Affiliation(s)
- Michael Wang
- Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, New York 10003, USA
| | - Alexander Y Grosberg
- Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, New York 10003, USA
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23
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Netz RR. Approach to equilibrium and nonequilibrium stationary distributions of interacting many-particle systems that are coupled to different heat baths. Phys Rev E 2020; 101:022120. [PMID: 32168558 DOI: 10.1103/physreve.101.022120] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 01/23/2020] [Indexed: 06/10/2023]
Abstract
A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and nonequilibrium stationary states. An equilibrium system is here defined as a system whose stationary distribution equals the Boltzmann distribution, the relation of this definition to the conditions of detailed balance and vanishing probability current is discussed both for underdamped as well as for overdamped systems. Based on the exactly calculated dynamic approach to the stationary distribution, the functional that governs this approach, which is called the free entropy S_{free}(t), is constructed. For the stationary distribution S_{free}(t) becomes maximal and its time derivative, the free entropy production S[over ̇]_{free}(t), is minimal and vanishes. Thus, S_{free}(t) characterizes equilibrium as well as nonequilibrium stationary distributions by their extremal and stability properties. For an equilibrium system, i.e., if all heat baths have the same temperature, the free entropy equals the negative free energy divided by temperature and thus corresponds to the Massieu function which was previously introduced in an alternative formulation of statistical mechanics. Using a systematic perturbative scheme for calculating velocity and position correlations in the overdamped massless limit, explicit results for few particles are presented: For two particles localization in position and momentum space is demonstrated in the nonequilibrium stationary state, indicative of a tendency to phase separate. For three elastically interacting particles heat flows from a particle coupled to a cold reservoir to a particle coupled to a warm reservoir if the third reservoir is sufficiently hot. This does not constitute a violation of the second law of thermodynamics, but rather demonstrates that a particle in such a nonequilibrium system is not characterized by an effective temperature which equals the temperature of the heat bath it is coupled to. Active particle models can be described in the same general framework, which thereby allows us to characterize their entropy production not only in the stationary state but also in the approach to the stationary nonequilibrium state. Finally, the connection to nonequilibrium thermodynamics formulations that include the reservoir entropy production is discussed.
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Affiliation(s)
- Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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24
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Abstract
In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by specific examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that, even in the fast switching limit, function out of equilibrium.
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25
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Abstract
We propose a generalization of stochastic thermodynamics to systems of active particles, which move under the combined influence of stochastic internal self-propulsions (activity) and a heat bath. The main idea is to consider joint trajectories of particles' positions and self-propulsions. It is then possible to exploit formal similarity of an active system and a system consisting of two subsystems interacting with different heat reservoirs and coupled by a nonsymmetric interaction. The resulting thermodynamic description closely follows the standard stochastic thermodynamics. In particular, total entropy production, Δs_{tot}, can be decomposed into housekeeping, Δs_{hk}, and excess, Δs_{ex}, parts. Both Δs_{tot} and Δs_{hk} satisfy fluctuation theorems. The average rate of the steady-state housekeeping entropy production can be related to the violation of the fluctuation-dissipation theorem via a Harada-Sasa relation. The excess entropy production enters into a Hatano-Sasa-like relation, which leads to a generalized Clausius inequality involving the change of the system's entropy and the excess entropy production. Interestingly, although the evolution of particles' self-propulsions is free and uncoupled from that of their positions, nontrivial steady-state correlations between these variables lead to the nonzero excess dissipation in the reservoir coupled to the self-propulsions.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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26
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Sarracino A, Vulpiani A. On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems. CHAOS (WOODBURY, N.Y.) 2019; 29:083132. [PMID: 31472486 DOI: 10.1063/1.5110262] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Accepted: 08/08/2019] [Indexed: 06/10/2023]
Abstract
We review generalized fluctuation-dissipation relations, which are valid under general conditions even in "nonstandard systems," e.g., out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperturbed dynamics. In these relations, typically, one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.
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Affiliation(s)
- A Sarracino
- Dipartimento di Ingegneria, Università della Campania "L. Vanvitelli," via Roma 29, 81031 Aversa (CE), Italy
| | - A Vulpiani
- Dipartimento di Fisica, Università Sapienza-p.le A. Moro 2, 00185 Roma, Italy
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27
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Grosberg AY, Joanny JF. Dissipation in a System Driven by Two Different Thermostats. POLYMER SCIENCE SERIES C 2018. [DOI: 10.1134/s1811238218020108] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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28
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Caprini L, Marconi UMB, Puglisi A, Vulpiani A. Comment on "Entropy Production and Fluctuation Theorems for Active Matter". PHYSICAL REVIEW LETTERS 2018; 121:139801. [PMID: 30312080 DOI: 10.1103/physrevlett.121.139801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Indexed: 06/08/2023]
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via F. Crispi 7, 67100 L'Aquila, Italy
| | | | - Andrea Puglisi
- Istituto dei Sistemi Complessi, CNR and Dipartimento di Fisica, Università di Roma Sapienza, Piazza le Aldo Moro 2, 00185 Rome, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica, Università Sapienza, Piazza le A. Moro 2, 00185 Roma, Italy and Centro Interdisciplinare "B. Segre," Accademia dei Lincei, 00165 Roma, Italy
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29
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Nakayama Y, Kawaguchi K, Nakagawa N. Unattainability of Carnot efficiency in thermal motors: Coarse graining and entropy production of Feynman-Smoluchowski ratchets. Phys Rev E 2018; 98:022102. [PMID: 30253614 DOI: 10.1103/physreve.98.022102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2018] [Indexed: 11/07/2022]
Abstract
We revisit and analyze the thermodynamic efficiency of the Feynman-Smoluchowski (FS) ratchet, a classical thought experiment describing an autonomous heat-work converter. Starting from the full kinetics of the FS ratchet and deriving the exact forms of the hidden dissipations resulting from coarse graining, we restate the historical controversy over its thermodynamic efficiency. The existence of hidden entropy productions implies that the standard framework of stochastic thermodynamics applied to the coarse-grained descriptions fails in capturing the dissipative feature of the system. In response to this problem, we explore an extended framework of stochastic thermodynamics to reconstruct the hidden entropy production from the coarse-grained dynamics. The approach serves as a key example of how we can systematically address the problem of thermodynamic efficiency in a multivariable fluctuating nonequilibrium system.
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Affiliation(s)
- Yohei Nakayama
- Department of Physics, Chuo University, Tokyo 112-8551, Japan
| | - Kyogo Kawaguchi
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, USA.,Universal Biology Institute, The University of Tokyo, Tokyo 113-0033, Japan
| | - Naoko Nakagawa
- Department of Physics, Ibaraki University, Mito 310-8512, Japan
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30
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Mancois V, Marcos B, Viot P, Wilkowski D. Two-temperature Brownian dynamics of a particle in a confining potential. Phys Rev E 2018; 97:052121. [PMID: 29906897 DOI: 10.1103/physreve.97.052121] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Indexed: 11/07/2022]
Abstract
We consider the two-dimensional motion of a particle in a confining potential, subject to Brownian orthogonal forces associated with two different temperatures. Exact solutions are obtained for an asymmetric harmonic potential in the overdamped and underdamped regimes. For more general confining potentials, a perturbative approach shows that the stationary state exhibits some universal properties. The nonequilibrium stationary state is characterized with a nonzero orthoradial mean current, corresponding to a global rotation of the particle around the center. The rotation is due to two broken symmetries: two different temperatures and a mismatch between the principal axes of the confining asymmetric potential and the temperature axes. We confirm our predictions by performing a Brownian dynamics simulation. Finally, we propose to observe this effect on a laser-cooled atomic gas.
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Affiliation(s)
- Vincent Mancois
- MajuLab, CNRS-Université de Nice-NUS-NTU International Joint Research Unit UMI 3654, Singapore.,PAP, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore.,Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Bruno Marcos
- Université Côte d'Azur, CNRS, LJAD, 06108 Nice, France
| | - Pascal Viot
- MajuLab, CNRS-Université de Nice-NUS-NTU International Joint Research Unit UMI 3654, Singapore.,Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - David Wilkowski
- MajuLab, CNRS-Université de Nice-NUS-NTU International Joint Research Unit UMI 3654, Singapore.,PAP, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore.,Centre for Quantum Technologies, National University of Singapore, 117543 Singapore
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31
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Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 116] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
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Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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32
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Netz RR. Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium. J Chem Phys 2018; 148:185101. [DOI: 10.1063/1.5020654] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roland R. Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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33
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Paul S, Laskar A, Singh R, Roy B, Adhikari R, Banerjee A. Direct verification of the fluctuation-dissipation relation in viscously coupled oscillators. Phys Rev E 2017; 96:050102. [PMID: 29347721 DOI: 10.1103/physreve.96.050102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2017] [Indexed: 06/07/2023]
Abstract
The fluctuation-dissipation relation, a central result in nonequilibrium statistical physics, relates equilibrium fluctuations in a system to its linear response to external forces. Here we provide a direct experimental verification of this relation for viscously coupled oscillators, as realized by a pair of optically trapped colloidal particles. A theoretical analysis, in which interactions mediated by slow viscous flow are represented by nonlocal friction tensors, matches experimental results and reveals a frequency maximum in the amplitude of the mutual response which is a sensitive function of the trap stiffnesses and the friction tensors. This allows for its location and width to be tuned and suggests the utility of the trap setup for accurate two-point microrheology.
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Affiliation(s)
- Shuvojit Paul
- Indian Institute of Science Education and Research, Kolkata, Mohanpur 741246, India
| | - Abhrajit Laskar
- The Institute of Mathematical Sciences-HBNI, CIT Campus, Taramani, Chennai 600113, India
| | - Rajesh Singh
- The Institute of Mathematical Sciences-HBNI, CIT Campus, Taramani, Chennai 600113, India
| | - Basudev Roy
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - R Adhikari
- The Institute of Mathematical Sciences-HBNI, CIT Campus, Taramani, Chennai 600113, India
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Ayan Banerjee
- Indian Institute of Science Education and Research, Kolkata, Mohanpur 741246, India
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34
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Clausius Relation for Active Particles: What Can We Learn from Fluctuations. ENTROPY 2017. [DOI: 10.3390/e19070356] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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35
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Crisanti A, Sarracino A, Zannetti M. Heat fluctuations of Brownian oscillators in nonstationary processes: Fluctuation theorem and condensation transition. Phys Rev E 2017; 95:052138. [PMID: 28618537 DOI: 10.1103/physreve.95.052138] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Indexed: 06/07/2023]
Abstract
We study analytically the probability distribution of the heat released by an ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium relaxation process following a temperature quench. We focus on the asymmetry properties of the heat distribution in the nonstationary dynamics, in order to study the forms taken by the fluctuation theorem as the number of degrees of freedom is varied. After analyzing in great detail the cases of one and two oscillators, we consider the limit of a large number of oscillators, where the behavior of fluctuations is enriched by a condensation transition with a nontrivial phase diagram, characterized by reentrant behavior. Numerical simulations confirm our analytical findings. We also discuss and highlight how concepts borrowed from the study of fluctuations in equilibrium under symmetry-breaking conditions [Gaspard, J. Stat. Mech. (2012) P0802110.1088/1742-5468/2012/08/P08021] turn out to be quite useful in understanding the deviations from the standard fluctuation theorem.
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Affiliation(s)
- A Crisanti
- Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185, Rome, Italy
- Istituto dei Sistemi Complessi-CNR, P.le Aldo Moro 2, 00185, Rome, Italy
| | - A Sarracino
- Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185, Rome, Italy
- Istituto dei Sistemi Complessi-CNR, P.le Aldo Moro 2, 00185, Rome, Italy
| | - M Zannetti
- Dipartimento di Fisica "E. R. Caianiello", Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
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36
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Heat, temperature and Clausius inequality in a model for active Brownian particles. Sci Rep 2017; 7:46496. [PMID: 28429787 PMCID: PMC5399351 DOI: 10.1038/srep46496] [Citation(s) in RCA: 62] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Accepted: 03/17/2015] [Indexed: 11/20/2022] Open
Abstract
Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system’s Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.
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37
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Bérut A, Imparato A, Petrosyan A, Ciliberto S. Theoretical description of effective heat transfer between two viscously coupled beads. Phys Rev E 2016; 94:052148. [PMID: 27967201 DOI: 10.1103/physreve.94.052148] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2016] [Indexed: 06/06/2023]
Abstract
We analytically study the role of nonconservative forces, namely viscous couplings, on the statistical properties of the energy flux between two Brownian particles kept at different temperatures. From the dynamical model describing the system, we identify an energy flow that satisfies a fluctuation theorem both in the stationary and in transient states. In particular, for the specific case of a linear nonconservative interaction, we derive an exact fluctuation theorem that holds for any measurement time in the transient regime, and which involves the energy flux alone. Moreover, in this regime the system presents an interesting asymmetry between the hot and cold particles. The theoretical predictions are in good agreement with the experimental results already presented in our previous article [Imparato et al., Phys. Rev. Lett. 116, 068301 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.068301], where we investigated the thermodynamic properties of two Brownian particles, trapped with optical tweezers, interacting through a dissipative hydrodynamic coupling.
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Affiliation(s)
- A Bérut
- Université de Lyon, CNRS, Laboratoire de Physique, École Normale Supérieure de Lyon (UMR5672), 46 Allée d'Italie, 69364 Lyon Cedex 07, France
| | - A Imparato
- Department of Physics and Astronomy, University of Aarhus Ny Munkegade, Building 1520, DK-8000 Aarhus C, Denmark
| | - A Petrosyan
- Université de Lyon, CNRS, Laboratoire de Physique, École Normale Supérieure de Lyon (UMR5672), 46 Allée d'Italie, 69364 Lyon Cedex 07, France
| | - S Ciliberto
- Université de Lyon, CNRS, Laboratoire de Physique, École Normale Supérieure de Lyon (UMR5672), 46 Allée d'Italie, 69364 Lyon Cedex 07, France
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38
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Chaudhuri D. Entropy production by active particles: Coupling of odd and even functions of velocity. Phys Rev E 2016; 94:032603. [PMID: 27739815 DOI: 10.1103/physreve.94.032603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2016] [Indexed: 06/06/2023]
Abstract
Nonequilibrium stochastic dynamics of several active Brownian systems are modeled in terms of nonlinear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for total entropy production in such systems using the Fokker-Planck equation. The result is consistent with the expression for stochastic entropy production in the reservoir that we obtain from probabilities of time-forward and time-reversed trajectories, leading to fluctuation theorems. Numerical simulation is used to find probability distribution of entropy production, which shows good agreement with the detailed fluctuation theorem.
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Affiliation(s)
- Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India and Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
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39
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Marino R, Eichhorn R, Aurell E. Entropy production of a Brownian ellipsoid in the overdamped limit. Phys Rev E 2016; 93:012132. [PMID: 26871049 DOI: 10.1103/physreve.93.012132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Indexed: 06/05/2023]
Abstract
We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.
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Affiliation(s)
- Raffaele Marino
- Nordita, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
| | - Ralf Eichhorn
- Nordita, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
| | - Erik Aurell
- Department of Computational Biology and ACCESS Linnaeus Centre and Center for Quantum Materials, KTH-Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden and Deptartments of Information and Computer Science and Applied Physics, Aalto University, Espoo, Finland
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40
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Lasanta A, Puglisi A. An itinerant oscillator model with cage inertia for mesorheological granular experiments. J Chem Phys 2015; 143:064511. [PMID: 26277149 DOI: 10.1063/1.4928456] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recent experiments with a rotating probe immersed in weakly fluidized granular materials show a complex behavior on a wide range of time scales. Viscous-like relaxation at high frequency is accompanied by an almost harmonic dynamical trapping at intermediate times, with possibly anomalous long time behavior in the form of super-diffusion. Inspired by the itinerant oscillator model for diffusion in molecular liquids, and other models with coupled thermostats acting at different time scales, here we discuss a new model able to account for fast viscous relaxation, dynamical trapping, and super-diffusion at long times. The main difference with respect to liquids is a non-negligible cage inertia for the surrounding (granular) fluid, which allows it to sustain a slow but persistent motion for long times. The computed velocity power density spectra and mean-squared displacement qualitatively reproduce the experimental findings. We also discuss the linear response to external perturbations and the tail of the distribution of persistency time, which is associated with superdiffusion, and whose cut-off time is determined by cage inertia.
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Affiliation(s)
- Antonio Lasanta
- CNR-ISC and Dipartimento di Fisica, Università La Sapienza, p.le A. Moro 2, 00185 Rome, Italy
| | - Andrea Puglisi
- CNR-ISC and Dipartimento di Fisica, Università La Sapienza, p.le A. Moro 2, 00185 Rome, Italy
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41
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Grosberg AY, Joanny JF. Nonequilibrium statistical mechanics of mixtures of particles in contact with different thermostats. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032118. [PMID: 26465437 DOI: 10.1103/physreve.92.032118] [Citation(s) in RCA: 83] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2015] [Indexed: 06/05/2023]
Abstract
We introduce a novel type of locally driven systems made of two types of particles (or a polymer with two types of monomers) subject to a chaotic drive with approximately white noise spectrum, but different intensity; in other words, particles of different types are in contact with thermostats at different temperatures. We present complete systematic statistical mechanics treatment starting from first principles. Although we consider only corrections to the dilute limit due to pairwise collisions between particles, meaning we study a nonequilibrium analog of the second virial approximation, we find that the system exhibits a surprisingly rich behavior. In particular, pair correlation function of particles has an unusual quasi-Boltzmann structure governed by an effective temperature distinct from that of any of the two thermostats. We also show that at sufficiently strong drive the uniformly mixed system becomes unstable with respect to steady states consisting of phases enriched with different types of particles. In the second virial approximation, we define nonequilibrium "chemical potentials" whose gradients govern diffusion fluxes and a nonequilibrium "osmotic pressure," which governs the mechanical stability of the interface.
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Affiliation(s)
- A Y Grosberg
- Physico-Chimie Curie UMR 168, Institut Curie, PSL Research University, 26 rue d'Ulm, 75248 Paris Cedex 05, France
- Department of Physics and Center for Soft Matter Research, New York University, 4 Washington Place, New York, New York 10003, USA
| | - J-F Joanny
- Physico-Chimie Curie UMR 168, Institut Curie, PSL Research University, 26 rue d'Ulm, 75248 Paris Cedex 05, France
- ESPCI-ParisTech, 10 rue Vauquelin 75005 Paris, France
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42
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Chun HM, Noh JD. Hidden entropy production by fast variables. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052128. [PMID: 26066140 DOI: 10.1103/physreve.91.052128] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2015] [Indexed: 06/04/2023]
Abstract
We investigate nonequilibrium underdamped Langevin dynamics of Brownian particles that interact through a harmonic potential with coupling constant K and are in thermal contact with two heat baths at different temperatures. The system is characterized by a net heat flow and an entropy production in the steady state. We compare the entropy production of the harmonic system with that of Brownian particles linked with a rigid rod. The harmonic system may be expected to reduce to the rigid rod system in the infinite K limit. However, we find that the harmonic system in the K→∞ limit produces more entropy than the rigid rod system. The harmonic system has the center-of-mass coordinate as a slow variable and the relative coordinate as a fast variable. By identifying the contributions of the degrees of freedom to the total entropy production, we show that the hidden entropy production by the fast variable is responsible for the extra entropy production. We discuss the K dependence of each contribution.
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Affiliation(s)
- Hyun-Myung Chun
- Department of Physics, University of Seoul, Seoul 130-743, Korea
| | - Jae Dong Noh
- Department of Physics, University of Seoul, Seoul 130-743, Korea
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
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43
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Rosinberg ML, Munakata T, Tarjus G. Stochastic thermodynamics of Langevin systems under time-delayed feedback control: Second-law-like inequalities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042114. [PMID: 25974446 DOI: 10.1103/physreve.91.042114] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2015] [Indexed: 06/04/2023]
Abstract
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.
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Affiliation(s)
- M L Rosinberg
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - T Munakata
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - G Tarjus
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
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44
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Lacoste D, Lomholt MA. Stochastic thermodynamics of a tagged particle within a harmonic chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022114. [PMID: 25768465 DOI: 10.1103/physreve.91.022114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2014] [Indexed: 06/04/2023]
Abstract
We study the stochastic thermodynamics of an overdamped harmonic chain, which can be viewed equivalently as a one-dimensional Rouse chain or as an approximate model of single file diffusion. We discuss mainly two levels of description of this system: the Markovian level for which the trajectories of all the particles of the chain are known and the non-Markovian level in which only the motion of a tagged particle is available. For each case, we analyze the energy dissipation and its dependence on initial conditions. Surprisingly, we find that the average coarse-grained entropy production rate can become transiently negative when an oscillating force is applied to the tagged particle. This occurs due to memory effects as shown in a framework based on path integrals or on a generalized Langevin equation.
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Affiliation(s)
- David Lacoste
- Laboratoire de Physico-Chimie Théorique - UMR CNRS Gulliver 7083, PSL Research University, ESPCI, 10 rue Vauquelin, F-75231 Paris, France
| | - Michael A Lomholt
- MEMPHYS-Center for Biomembrane Physics, Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
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45
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Zimmermann E, Seifert U. Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022709. [PMID: 25768533 DOI: 10.1103/physreve.91.022709] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
Many single-molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the F(1)-ATPase and the kinesin motor.
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Affiliation(s)
- Eva Zimmermann
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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46
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Pal A, Sabhapandit S. Work fluctuations for a Brownian particle driven by a correlated external random force. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052116. [PMID: 25493749 DOI: 10.1103/physreve.90.052116] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2014] [Indexed: 06/04/2023]
Abstract
We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external force on the Brownian particle in a given time interval in the steady state. We calculate the large deviation functions as well as the complete asymptotic form of the probability density function of the performed work. We also discuss the symmetry properties of the large deviation functions for this system. Finally we perform numerical simulations and they are in a very good agreement with the analytic results.
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Affiliation(s)
- Arnab Pal
- Raman Research Institute, Bangalore 560080, India
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47
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Conti L, Lazzaro C, Karapetyan G, Bonaldi M, Pegoraro M, Thakur RK, De Gregorio P, Rondoni L. Thermal noise of mechanical oscillators in steady states with a heat flux. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032119. [PMID: 25314407 DOI: 10.1103/physreve.90.032119] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2014] [Indexed: 06/04/2023]
Abstract
We present an experimental investigation of the statistical properties of the position fluctuations of low-loss oscillators in nonequilibrium steady states. The oscillators are coupled to a heat bath, and a nonequilibrium steady state is produced by flowing a constant heat flux, setting a temperature difference across the oscillators. We investigated the distribution of the measurements of the square of the oscillator position and searched for signs of changes with respect to the equilibrium case. We found that, after normalization by the mean value, the second, third, and fourth standardized statistical moments are not modified by the underlying thermodynamic state. This differs from the behavior of the absolute, i.e., not normalized, second moment, which is strongly affected by temperature gradients and heat fluxes. We illustrate this with a numerical experiment in which we study via molecular dynamics the fluctuations of the length of a one-dimensional chain of identical particles interacting via anharmonic interparticle potentials, with the extremes thermostated at different temperatures: we use the variance of the length in correspondence to its first elastic mode of resonance to define an effective temperature which we observe to depart from the thermodynamic one in the nonequilibrium states. We investigate the effect of changing the interparticle potential and show that the qualitative behavior of the nonequilibrium excess is unchanged. Our numerical results are consistent with the chain length being Gaussian distributed in the nonequilibrium states. Our experimental investigation reveals that the position variance is the only, and crucially easily accessible, observable for distinguishing equilibrium from nonequilibrium steady states. The consequences of this fact for the design of interferometric gravitational wave detectors are discussed.
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Affiliation(s)
- Livia Conti
- Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy
| | - Claudia Lazzaro
- Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy
| | - Gagik Karapetyan
- Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy
| | - Michele Bonaldi
- Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division, 38123 Povo (Trento), Italy and Istituto Nazionale di Fisica Nucleare, Trento Institute for Fundamental Physics and Applications, 38123 Povo (Trento), Italy
| | - Matteo Pegoraro
- Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy
| | - Ram-Krishna Thakur
- Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy
| | - Paolo De Gregorio
- Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche and Graphene@PoliTO Lab, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giura 1, 10125 Torino, Italy
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48
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Munakata T, Rosinberg ML. Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control. PHYSICAL REVIEW LETTERS 2014; 112:180601. [PMID: 24856682 DOI: 10.1103/physrevlett.112.180601] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2014] [Indexed: 06/03/2023]
Abstract
Continuous feedback control of Langevin processes may be non-Markovian due to a time lag between the measurement and the control action. We show that this requires one to modify the basic relation between dissipation and time reversal and to include a contribution arising from the noncausal character of the reverse process. We then propose a new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state, which can also be regarded as the trajectory-dependent total entropy production. This leads to an extension of the second law, which takes a simple form in the long-time limit. As an illustration, we apply the general approach to linear systems that are both analytically tractable and experimentally relevant.
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Affiliation(s)
- T Munakata
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - M L Rosinberg
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 Place Jussieu, 75252 Paris Cedex 05, France
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49
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50
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Muy S, Kundu A, Lacoste D. Non-invasive estimation of dissipation from non-equilibrium fluctuations in chemical reactions. J Chem Phys 2013; 139:124109. [DOI: 10.1063/1.4821760] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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