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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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Loos SAM, Arabha S, Rajabpour A, Hassanali A, Roldán É. Nonreciprocal forces enable cold-to-hot heat transfer between nanoparticles. Sci Rep 2023; 13:4517. [PMID: 36934145 PMCID: PMC10024720 DOI: 10.1038/s41598-023-31583-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 03/14/2023] [Indexed: 03/20/2023] Open
Abstract
We study the heat transfer between two nanoparticles held at different temperatures that interact through nonreciprocal forces, by combining molecular dynamics simulations with stochastic thermodynamics. Our simulations reveal that it is possible to construct nano refrigerators that generate a net heat transfer from a cold to a hot reservoir at the expense of power exerted by the nonreciprocal forces. Applying concepts from stochastic thermodynamics to a minimal underdamped Langevin model, we derive exact analytical expressions predictions for the fluctuations of work, heat, and efficiency, which reproduce thermodynamic quantities extracted from the molecular dynamics simulations. The theory only involves a single unknown parameter, namely an effective friction coefficient, which we estimate fitting the results of the molecular dynamics simulation to our theoretical predictions. Using this framework, we also establish design principles which identify the minimal amount of entropy production that is needed to achieve a certain amount of uncertainty in the power fluctuations of our nano refrigerator. Taken together, our results shed light on how the direction and fluctuations of heat flows in natural and artificial nano machines can be accurately quantified and controlled by using nonreciprocal forces.
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Affiliation(s)
- Sarah A M Loos
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK.
- ICTP - International Centre for Theoretical Physics, Strada Costiera, 11, 34151, Trieste, Italy.
| | - Saeed Arabha
- Department of Mechanical Engineering, Lassonde School of Engineering, York University, Toronto, Canada
- Advanced Simulation and Computing Laboratory (ASCL), Imam Khomeini International University, Qazvin, Iran
| | - Ali Rajabpour
- Advanced Simulation and Computing Laboratory (ASCL), Imam Khomeini International University, Qazvin, Iran
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
| | - Ali Hassanali
- ICTP - International Centre for Theoretical Physics, Strada Costiera, 11, 34151, Trieste, Italy
| | - Édgar Roldán
- ICTP - International Centre for Theoretical Physics, Strada Costiera, 11, 34151, Trieste, Italy
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Feng M, Hou Z. Mode-coupling theory for the dynamics of dense underdamped active Brownian particle system. J Chem Phys 2023; 158:024102. [PMID: 36641396 DOI: 10.1063/5.0131080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We present a theory to study the inertial effect on glassy dynamics of the underdamped active Brownian particle (UABP) system. Using the assumption of the nonequilibrium steady-state, we obtain an effective Fokker-Planck equation for the probability distribution function (PDF) as a function of positions and momentums. With this equation, we achieve the evolution equation of the intermediate scattering function through the Zwanzig-Mori projection operator method and the mode-coupling theory (MCT). Theoretical analysis shows that the inertia of the particle affects the memory function and corresponding glass transition by influencing the structure factor and a velocity correlation function. The theory provides theoretical support and guidance for subsequent simulation work.
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Affiliation(s)
- Mengkai Feng
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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Abdoli I, Wittmann R, Brader JM, Sommer JU, Löwen H, Sharma A. Tunable Brownian magneto heat pump. Sci Rep 2022; 12:13405. [PMID: 35927292 PMCID: PMC9352690 DOI: 10.1038/s41598-022-17584-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 07/27/2022] [Indexed: 11/09/2022] Open
Abstract
We propose a mesoscopic Brownian magneto heat pump made of a single charged Brownian particle that is steered by an external magnetic field. The particle is subjected to two thermal noises from two different heat sources. When confined, the particle performs gyrating motion around a potential energy minimum. We show that such a magneto-gyrator can be operated as both a heat engine and a refrigerator. The maximum power delivered by the engine and the performance of the refrigerator, namely the rate of heat transferred per unit external work, can be tuned and optimised by the applied magnetic field. Further tunability of the key properties of the engine, such as the direction of gyration and the torque exerted by the engine on the confining potential, is obtained by varying the strength and direction of the applied magnetic field. In principle, our predictions can be tested by experiments with colloidal particles and complex plasmas.
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Affiliation(s)
- Iman Abdoli
- Institut Theorie der Polymere, Leibniz-Institut für Polymerforschung Dresden, 01069, Dresden, Germany.,Institut für Theoretische Physik, Technische Universität Dresden, 01069, Dresden, Germany
| | - René Wittmann
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225, Düsseldorf, Germany
| | | | - Jens-Uwe Sommer
- Institut Theorie der Polymere, Leibniz-Institut für Polymerforschung Dresden, 01069, Dresden, Germany.,Institut für Theoretische Physik, Technische Universität Dresden, 01069, Dresden, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225, Düsseldorf, Germany
| | - Abhinav Sharma
- Institut Theorie der Polymere, Leibniz-Institut für Polymerforschung Dresden, 01069, Dresden, Germany. .,Institut für Theoretische Physik, Technische Universität Dresden, 01069, Dresden, Germany.
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Marbach S, Holmes-Cerfon M. Mass Changes the Diffusion Coefficient of Particles with Ligand-Receptor Contacts in the Overdamped Limit. PHYSICAL REVIEW LETTERS 2022; 129:048003. [PMID: 35939031 DOI: 10.1103/physrevlett.129.048003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Revised: 03/29/2022] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
Inertia does not generally affect the long-time diffusion of passive overdamped particles in fluids. Yet a model starting from the Langevin equation predicts a surprising property of particles coated with ligands that bind reversibly to surface receptors: heavy particles diffuse more slowly than light ones of the same size. We show this by simulation and by deriving an analytic formula for the mass-dependent diffusion coefficient in the overdamped limit. We estimate the magnitude of this effect for a range of biophysical ligand-receptor systems, and find it is potentially observable for tailored micronscale DNA-coated colloids.
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Affiliation(s)
- Sophie Marbach
- Courant Institute of Mathematical Sciences, New York University, New York 10012, USA
- CNRS, Sorbonne Université, Physicochimie des Electrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Miranda Holmes-Cerfon
- Courant Institute of Mathematical Sciences, New York University, New York 10012, USA
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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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Asheichyk K, Fuchs M, Krüger M. Brownian systems perturbed by mild shear: comparing response relations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:405101. [PMID: 34139676 DOI: 10.1088/1361-648x/ac0c3c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 06/17/2021] [Indexed: 06/12/2023]
Abstract
We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.
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Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
- Department of Theoretical Physics and Astrophysics, Belarusian State University, 5 Babruiskaya St., 220006 Minsk, Belarus
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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