1
|
Wang Z, Ren J. Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport. PHYSICAL REVIEW LETTERS 2024; 132:207101. [PMID: 38829089 DOI: 10.1103/physrevlett.132.207101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Revised: 09/06/2023] [Accepted: 04/11/2024] [Indexed: 06/05/2024]
Abstract
Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.
Collapse
Affiliation(s)
- Zi Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| |
Collapse
|
2
|
Tesser L, Splettstoesser J. Out-of-Equilibrium Fluctuation-Dissipation Bounds. PHYSICAL REVIEW LETTERS 2024; 132:186304. [PMID: 38759166 DOI: 10.1103/physrevlett.132.186304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 04/02/2024] [Indexed: 05/19/2024]
Abstract
We prove a general inequality between the charge current and its fluctuations valid for any weakly interacting coherent electronic conductor and for any stationary out-of-equilibrium condition, thereby going beyond established fluctuation-dissipation relations. The developed fluctuation-dissipation bound saturates at large temperature bias and reveals additional insight for heat engines, since it limits the output power by power fluctuations. It is valid when the thermodynamic uncertainty relations break down due to quantum effects and provides stronger constraints close to thermovoltage.
Collapse
Affiliation(s)
- Ludovico Tesser
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96 Göteborg, Sweden
| | - Janine Splettstoesser
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96 Göteborg, Sweden
| |
Collapse
|
3
|
Hasegawa Y. Thermodynamic Correlation Inequality. PHYSICAL REVIEW LETTERS 2024; 132:087102. [PMID: 38457724 DOI: 10.1103/physrevlett.132.087102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Revised: 08/09/2023] [Accepted: 01/23/2024] [Indexed: 03/10/2024]
Abstract
Trade-off relations place fundamental limits on the operations that physical systems can perform. This Letter presents a trade-off relation that bounds the correlation function, which measures the relationship between a system's current and future states, in Markov processes. The obtained bound, referred to as the thermodynamic correlation inequality, states that the change in the correlation function has an upper bound comprising the dynamical activity, a thermodynamic measure of the activity of a Markov process. Moreover, by applying the obtained relation to the linear response function, it is demonstrated that the effect of perturbation can be bounded from above by the dynamical activity.
Collapse
Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
4
|
Aslyamov T, Esposito M. Nonequilibrium Response for Markov Jump Processes: Exact Results and Tight Bounds. PHYSICAL REVIEW LETTERS 2024; 132:037101. [PMID: 38307069 DOI: 10.1103/physrevlett.132.037101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Revised: 10/13/2023] [Accepted: 12/14/2023] [Indexed: 02/04/2024]
Abstract
Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the static response of nonequilibrium steady state to arbitrary perturbations. This allows us to derive explicit expressions for the response of edge currents as well as traffic to perturbations in kinetic barriers and driving forces. We also show that these responses satisfy very simple bounds. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods.
Collapse
Affiliation(s)
- Timur Aslyamov
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| |
Collapse
|
5
|
Bakewell-Smith G, Girotti F, Guţă M, Garrahan JP. General Upper Bounds on Fluctuations of Trajectory Observables. PHYSICAL REVIEW LETTERS 2023; 131:197101. [PMID: 38000415 DOI: 10.1103/physrevlett.131.197101] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2022] [Accepted: 09/21/2023] [Indexed: 11/26/2023]
Abstract
Thermodynamic uncertainty relations (TURs) are general lower bounds on the size of fluctuations of dynamical observables. They have important consequences, one being that the precision of estimation of a current is limited by the amount of entropy production. Here, we prove the existence of general upper bounds on the size of fluctuations of any linear combination of fluxes (including all time-integrated currents or dynamical activities) for continuous-time Markov chains. We obtain these general relations by means of concentration bound techniques. These "inverse TURs" are valid for all times and not only in the long time limit. We illustrate our analytical results with a simple model, and discuss wider implications of these new relations.
Collapse
Affiliation(s)
- George Bakewell-Smith
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Federico Girotti
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Department of Mathematics, Polytechnic University of Milan, Milan, Piazza Leonardo da Vinci 32, 20133, Italy
| | - Mădălin Guţă
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
6
|
Ray KJ, Boyd AB, Guarnieri G, Crutchfield JP. Thermodynamic uncertainty theorem. Phys Rev E 2023; 108:054126. [PMID: 38115447 DOI: 10.1103/physreve.108.054126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 09/11/2023] [Indexed: 12/21/2023]
Abstract
Thermodynamic uncertainty relations (TURs) express a fundamental lower bound on the precision (inverse scaled variance) of any thermodynamic charge-e.g., work or heat-by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend TUR inequalities by incorporating and analyzing the impact of higher statistical cumulants of the entropy production itself within the general framework of time-symmetrically-controlled computation. We derive an exact expression for the charge that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name the thermodynamic uncertainty theorem (TUT). Importantly, both the minimum scaled variance charge and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any charge's precision. This is made explicit via a thorough numerical analysis of "swap" and "reset" computations that quantitatively compares the TUT against previous generalized TURs.
Collapse
Affiliation(s)
- Kyle J Ray
- Complexity Sciences Center and Department of Physics and Astronomy, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
| | - Alexander B Boyd
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, USA
- School of Physics, Trinity College Dublin, College Green, Dublin 2, D02 PN40, Ireland
| | - Giacomo Guarnieri
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - James P Crutchfield
- Complexity Sciences Center and Department of Physics and Astronomy, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
| |
Collapse
|
7
|
Fernandes Martins G, Horowitz JM. Topologically constrained fluctuations and thermodynamics regulate nonequilibrium response. Phys Rev E 2023; 108:044113. [PMID: 37978593 DOI: 10.1103/physreve.108.044113] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 08/07/2023] [Indexed: 11/19/2023]
Abstract
The limits on a system's response to external perturbations inform our understanding of how physical properties can be shaped by microscopic characteristics. Here, we derive constraints on the steady-state nonequilibrium response of physical observables in terms of the topology of the microscopic state space and the strength of thermodynamic driving. Notably, evaluation of these limits requires no kinetic information beyond the state-space structure. When applied to models of receptor binding, we find that sensitivity is bounded by the steepness of a Hill function with a Hill coefficient enhanced by the chemical driving beyond the structural equilibrium limit.
Collapse
Affiliation(s)
| | - Jordan M Horowitz
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
| |
Collapse
|
8
|
Nishiyama T, Hasegawa Y. Upper bound for entropy production in Markov processes. Phys Rev E 2023; 108:044139. [PMID: 37978718 DOI: 10.1103/physreve.108.044139] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Accepted: 10/04/2023] [Indexed: 11/19/2023]
Abstract
The second law of thermodynamics states that entropy production cannot be negative. Recent developments concerning uncertainty relations in stochastic thermodynamics, such as thermodynamic uncertainty relations and speed limits, have yielded refined second laws that provide lower bounds of entropy production by incorporating information from current statistics or distributions. In contrast, in this study we bound the entropy production from above by terms comprising the dynamical activity and maximum transition-rate ratio. We derive two upper bounds: One applies to steady-state conditions, whereas the other applies to arbitrary time-dependent conditions. We verify these bounds through numerical simulation and identify several potential applications.
Collapse
Affiliation(s)
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
9
|
Salazar DSP. Thermodynamic variational relation. Phys Rev E 2023; 108:044103. [PMID: 37978589 DOI: 10.1103/physreve.108.044103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Accepted: 09/07/2023] [Indexed: 11/19/2023]
Abstract
In systems far from equilibrium, the statistics of observables are connected to entropy production, leading to the thermodynamic uncertainty relation (TUR). However, the derivation of TURs often involves constraining the parity of observables, such as considering asymmetric currents, making it unsuitable for the general case. We propose a thermodynamic variational relation (TVR) between the statistics of general observables and entropy production, based on the variational representation of f divergences. From this result, we derive a universal TUR and other relations for higher-order statistics of observables.
Collapse
Affiliation(s)
- Domingos S P Salazar
- Unidade de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil
| |
Collapse
|
10
|
Pal PS, Pal A, Park H, Lee JS. Thermodynamic trade-off relation for first passage time in resetting processes. Phys Rev E 2023; 108:044117. [PMID: 37978646 DOI: 10.1103/physreve.108.044117] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 09/14/2023] [Indexed: 11/19/2023]
Abstract
Resetting is a strategy for boosting the speed of a target-searching process. Since its introduction over a decade ago, most studies have been carried out under the assumption that resetting takes place instantaneously. However, due to its irreversible nature, resetting processes incur a thermodynamic cost, which becomes infinite in the case of instantaneous resetting. Here, we take into consideration both the cost and the first passage time (FPT) required for a resetting process, in which the reset or return to the initial location is implemented using a trapping potential over a finite but random time period. An iterative generating function and a counting functional method à la Feynman and Kac are employed to calculate the FPT and the average work for this process. From these results, we obtain an explicit form of the time-cost trade-off relation, which provides the lower bound of the mean FPT for a given work input when the trapping potential is linear. This trade-off relation clearly shows that instantaneous resetting is achievable only when an infinite amount of work is provided. More surprisingly, the trade-off relation derived from the linear potential seems to be valid for a wide range of trapping potentials. In addition, we have also shown that the fixed-time or sharp resetting can further enhance the trade-off relation compared to that of the stochastic resetting.
Collapse
Affiliation(s)
- P S Pal
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Hyunggyu Park
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Jae Sung Lee
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| |
Collapse
|
11
|
Shiraishi N. Entropy production limits all fluctuation oscillations. Phys Rev E 2023; 108:L042103. [PMID: 37978716 DOI: 10.1103/physreve.108.l042103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 10/03/2023] [Indexed: 11/19/2023]
Abstract
The oscillation of fluctuation with two state observables is investigated. Following the idea of Ohga et al. [Phys. Rev. Lett. 131, 077101 (2023)10.1103/PhysRevLett.131.077101], we find that the fluctuation oscillation relative to their autocorrelations is bounded from above by the entropy production per characteristic maximum oscillation time. Our result applies to a variety of systems including Langevin systems, chemical reaction systems, and macroscopic systems. In addition, our bound consists of experimentally tractable quantities, which enables us to examine our inequality experimentally.
Collapse
Affiliation(s)
- Naoto Shiraishi
- Faculty of arts and sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902, Japan
| |
Collapse
|
12
|
van der Meer J, Degünther J, Seifert U. Time-Resolved Statistics of Snippets as General Framework for Model-Free Entropy Estimators. PHYSICAL REVIEW LETTERS 2023; 130:257101. [PMID: 37418719 DOI: 10.1103/physrevlett.130.257101] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 02/20/2023] [Accepted: 06/07/2023] [Indexed: 07/09/2023]
Abstract
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time reversal like a current. We introduce a general framework that allows us to infer a lower bound on entropy production through measuring the time-resolved statistics of events with any symmetry under time reversal, in particular, time-symmetric instantaneous events. We emphasize Markovianity as a property of certain events rather than of the full system and introduce an operationally accessible criterion for this weakened Markov property. Conceptually, the approach is based on snippets as particular sections of trajectories between two Markovian events, for which a generalized detailed balance relation is discussed.
Collapse
Affiliation(s)
- Jann van der Meer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Julius Degünther
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
13
|
Hasegawa Y. Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence. Nat Commun 2023; 14:2828. [PMID: 37198163 DOI: 10.1038/s41467-023-38074-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 04/13/2023] [Indexed: 05/19/2023] Open
Abstract
The bulk-boundary correspondence provides a guiding principle for tackling strongly correlated and coupled systems. In the present work, we apply the concept of the bulk-boundary correspondence to thermodynamic bounds described by classical and quantum Markov processes. Using the continuous matrix product state, we convert a Markov process to a quantum field, such that jump events in the Markov process are represented by the creation of particles in the quantum field. Introducing the time evolution of the continuous matrix product state, we apply the geometric bound to its time evolution. We find that the geometric bound reduces to the speed limit relation when we represent the bound in terms of the system quantity, whereas the same bound reduces to the thermodynamic uncertainty relation when expressed based on quantities of the quantum field. Our results show that the speed limits and thermodynamic uncertainty relations are two aspects of the same geometric bound.
Collapse
Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, 113-8656, Japan.
| |
Collapse
|
14
|
Chun HM, Horowitz JM. Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks. J Chem Phys 2023; 158:2888610. [PMID: 37144710 DOI: 10.1063/5.0148662] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 04/17/2023] [Indexed: 05/06/2023] Open
Abstract
We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations and the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to sensitively depend on the deficiency of the network.
Collapse
Affiliation(s)
- Hyun-Myung Chun
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Jordan M Horowitz
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| |
Collapse
|
15
|
Kamijima T, Ito S, Dechant A, Sagawa T. Thermodynamic uncertainty relations for steady-state thermodynamics. Phys Rev E 2023; 107:L052101. [PMID: 37329003 DOI: 10.1103/physreve.107.l052101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Accepted: 04/20/2023] [Indexed: 06/18/2023]
Abstract
A system can be driven out of equilibrium by both time-dependent and nonconservative forces, which gives rise to a decomposition of the dissipation into two nonnegative components, called the excess and housekeeping entropy productions. We derive thermodynamic uncertainty relations for the excess and housekeeping entropy. These can be used as tools to estimate the individual components, which are in general difficult to measure directly. We introduce a decomposition of an arbitrary current into housekeeping and excess parts, which provide lower bounds on the respective entropy production. Furthermore, we also provide a geometric interpretation of the decomposition and show that the uncertainties of the two components are not independent, but rather have to obey a joint uncertainty relation, which also yields a tighter bound on the total entropy production. We apply our results to a paradigmatic example that illustrates the physical interpretation of the components of the current and how to estimate the entropy production.
Collapse
Affiliation(s)
- Takuya Kamijima
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Sosuke Ito
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Andreas Dechant
- Department of Physics No. 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Quantum-Phase Electronics Center (QPEC), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|
16
|
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: 0] [Impact Index Per Article: 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.
Collapse
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
| |
Collapse
|
17
|
Dieball C, Godec A. Direct Route to Thermodynamic Uncertainty Relations and Their Saturation. PHYSICAL REVIEW LETTERS 2023; 130:087101. [PMID: 36898097 DOI: 10.1103/physrevlett.130.087101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Revised: 11/23/2022] [Accepted: 01/12/2023] [Indexed: 06/18/2023]
Abstract
Thermodynamic uncertainty relations (TURs) bound the dissipation in nonequilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly from the Langevin equation. This establishes the TUR as an inherent property of overdamped stochastic equations of motion. In addition, we extend the transient TUR to currents and densities with explicit time dependence. By including current-density correlations we, moreover, derive a new sharpened TUR for transient dynamics. Our arguably simplest and most direct proof, together with the new generalizations, allows us to systematically determine conditions under which the different TURs saturate and thus allows for a more accurate thermodynamic inference. Finally, we outline the direct proof also for Markov jump dynamics.
Collapse
Affiliation(s)
- Cai Dieball
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
| |
Collapse
|
18
|
Bao R, Hou Z. Improving estimation of entropy production rate for run-and-tumble particle systems by high-order thermodynamic uncertainty relation. Phys Rev E 2023; 107:024112. [PMID: 36932577 DOI: 10.1103/physreve.107.024112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 01/30/2023] [Indexed: 02/12/2023]
Abstract
Entropy production plays an important role in the regulation and stability of active matter systems, and its rate quantifies the nonequilibrium nature of these systems. However, entropy production is hard to experimentally estimate even in some simple active systems like molecular motors or bacteria, which may be modeled by the run-and-tumble particle (RTP), a representative model in the study of active matters. Here we resolve this problem for an asymmetric RTP in one dimension, first constructing a finite-time thermodynamic uncertainty relation (TUR) for a RTP, which works well in the short observation time regime for entropy production estimation. Nevertheless, when the activity dominates, i.e., the RTP is far from equilibrium, the lower bound for entropy production from TUR turns out to be trivial. We address this issue by introducing a recently proposed high-order thermodynamic uncertainty relation (HTUR), in which the cumulant generating function of current serves as a key ingredient. To exploit the HTUR, we adopt a method to analytically obtain the cumulant generating function of the current we study, with no need to explicitly know the time-dependent probability distribution. The HTUR is demonstrated to be able to estimate the steady state energy dissipation rate accurately because the cumulant generating function covers higher-order statistics of the current, including rare and large fluctuations besides its variance. Compared to the conventional TUR, the HTUR could give significantly improved estimation of energy dissipation, which can work well even in the far from equilibrium regime. We also provide a strategy based on the improved bound to estimate the entropy production from a moderate amount of trajectory data for experimental feasibility.
Collapse
Affiliation(s)
- Ruicheng Bao
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| |
Collapse
|
19
|
Salazar DSP. Thermodynamic uncertainty relation from involutions. Phys Rev E 2022; 106:L062104. [PMID: 36671130 DOI: 10.1103/physreve.106.l062104] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Accepted: 12/09/2022] [Indexed: 06/17/2023]
Abstract
The thermodynamic uncertainty relation (TUR) is a lower bound for the variance of a current (over the mean squared) as a function of the average entropy production. Depending on the assumptions, one obtains different versions of the TUR. For instance, from the exchange fluctuation theorem, one obtains a corresponding exchange TUR. Alternatively, we show that TURs are a consequence of a very simple property: Every process s has only one conjugate s^{'}=m(s), where m is an involution, m(m(s))=s. This property allows the derivation of a general TUR without using any fluctuation theorem. As applications, we obtain the exchange TUR, the hysteretic TUR, a fluctuation-response inequality and a lower bound for the entropy production in terms of other nonequilibrium metrics.
Collapse
Affiliation(s)
- Domingos S P Salazar
- Unidade de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil
| |
Collapse
|
20
|
Polettini M, Falasco G, Esposito M. Tight uncertainty relations for cycle currents. Phys Rev E 2022; 106:064121. [PMID: 36671076 DOI: 10.1103/physreve.106.064121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 11/23/2022] [Indexed: 12/23/2022]
Abstract
Several recent inequalities bound the precision of a current, i.e., a counter of the net number of transitions in a system, by a thermodynamic measure of dissipation. However, while currents may be defined locally, dissipation is a global property. Inspired by the fact that, ever since Carnot, cycles are the unit elements of thermodynamic processes, we prove similar bounds tailored to cycle currents, counting net cycle completions, in terms of their conjugate affinities. We show that these inequalities are stricter than previous ones, even far from equilibrium, and that they allow us to tighten those on transition currents. We illustrate our results with a simple model and discuss some technical and conceptual issues related to shifting attention from transition to cycle observables.
Collapse
Affiliation(s)
- Matteo Polettini
- Department of Physics and Materials Science, University of Luxembourg, Campus Limpertsberg, 162a Avenue de la Faïencerie, 1511 Luxembourg, Grand Duchy of Luxembourg
| | - Gianmaria Falasco
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, Campus Limpertsberg, 162a Avenue de la Faïencerie, 1511 Luxembourg, Grand Duchy of Luxembourg
| |
Collapse
|
21
|
Koyuk T, Seifert U. Thermodynamic Uncertainty Relation in Interacting Many-Body Systems. PHYSICAL REVIEW LETTERS 2022; 129:210603. [PMID: 36461951 DOI: 10.1103/physrevlett.129.210603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 06/01/2022] [Accepted: 10/06/2022] [Indexed: 06/17/2023]
Abstract
The thermodynamic uncertainty relation (TUR) has been well studied for systems with few degrees of freedom. While, in principle, the TUR holds for more complex systems with many interacting degrees of freedom as well, little is known so far about its behavior in such systems. We analyze the TUR in the thermodynamic limit for mixtures of driven particles with short-range interactions. Our main result is an explicit expression for the optimal estimate of the total entropy production in terms of single-particle currents and correlations between two-particle currents. Quantitative results for various versions of a driven lattice gas demonstrate the practical implementation of this approach.
Collapse
Affiliation(s)
- Timur Koyuk
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
22
|
Lee JS, Lee S, Kwon H, Park H. Speed Limit for a Highly Irreversible Process and Tight Finite-Time Landauer's Bound. PHYSICAL REVIEW LETTERS 2022; 129:120603. [PMID: 36179191 DOI: 10.1103/physrevlett.129.120603] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
Landauer's bound is the minimum thermodynamic cost for erasing one bit of information. As this bound is achievable only for quasistatic processes, finite-time operation incurs additional energetic costs. We find a tight finite-time Landauer's bound by establishing a general form of the classical speed limit. This tight bound well captures the divergent behavior associated with the additional cost of a highly irreversible process, which scales differently from a nearly irreversible process. We also find an optimal dynamics which saturates the equality of the bound. We demonstrate the validity of this bound via discrete one-bit and coarse-grained bit systems. Our Letter implies that more heat dissipation than expected occurs during high-speed irreversible computation.
Collapse
Affiliation(s)
- Jae Sung Lee
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Sangyun Lee
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyukjoon Kwon
- School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunggyu Park
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| |
Collapse
|
23
|
Dechant A, Sasa SI, Ito S. Geometric decomposition of entropy production into excess, housekeeping, and coupling parts. Phys Rev E 2022; 106:024125. [PMID: 36109899 DOI: 10.1103/physreve.106.024125] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
For a generic overdamped Langevin dynamics driven out of equilibrium by both time-dependent and nonconservative forces, the entropy production rate can be decomposed into two positive terms, termed excess and housekeeping entropy. However, this decomposition is not unique: There are two distinct decompositions, one due to Hatano and Sasa, the other one due to Maes and Netočný. Here we establish the connection between these two decompositions and provide a simple, geometric interpretation. We show that this leads to a decomposition of the entropy production rate into three positive terms, which we call the excess, housekeeping, and coupling part, respectively. The coupling part characterizes the interplay between the time-dependent and nonconservative forces. We also derive thermodynamic uncertainty relations for the excess and housekeeping entropy in both the Hatano-Sasa and Maes-Netočný decomposition and show that all quantities obey integral fluctuation theorems. We illustrate the decomposition into three terms using a solvable example of a dragged particle in a nonconservative force field.
Collapse
Affiliation(s)
- Andreas Dechant
- Department of Physics no. 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Shin-Ichi Sasa
- Department of Physics no. 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Sosuke Ito
- Universal Biology Institute, The University of Tokyo, Tokyo 113-0033, Japan
- JST, PRESTO, Saitama 332-0012, Japan
| |
Collapse
|
24
|
Shiraishi N. Time-Symmetric Current and Its Fluctuation Response Relation around Nonequilibrium Stalling Stationary State. PHYSICAL REVIEW LETTERS 2022; 129:020602. [PMID: 35867465 DOI: 10.1103/physrevlett.129.020602] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Revised: 04/15/2022] [Accepted: 06/13/2022] [Indexed: 06/15/2023]
Abstract
We propose a time-symmetric counterpart of the current in stochastic thermodynamics named the time-symmetric current. This quantity is defined with empirical measures and thus is symmetric under time reversal, while its ensemble average reproduces the amount of the average current. We prove that this time-symmetric current satisfies the fluctuation-response relation in the conventional form but with sign inversion. Remarkably, this fluctuation-response relation holds not only around equilibrium states but also around nonequilibrium stationary states if observed currents stall. The obtained relation also serves as an experimental tool for probing the value of a bare transition rate by measuring only time-integrated empirical measures.
Collapse
Affiliation(s)
- Naoto Shiraishi
- Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
| |
Collapse
|
25
|
Ertel B, van der Meer J, Seifert U. Operationally accessible uncertainty relations for thermodynamically consistent semi-Markov processes. Phys Rev E 2022; 105:044113. [PMID: 35590600 DOI: 10.1103/physreve.105.044113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium imposes a crucial condition called direction-time independence for which we present an alternative derivation. We prove a thermodynamic uncertainty relation that formally resembles the one for a discrete-time Markov process. The result relates the entropy production of the semi-Markov process to mean and variance of steady-state currents. We prove a further thermodynamic uncertainty relation valid for semi-Markov descriptions of coarse-grained Markov processes that emerge by grouping states together. A violation of this inequality can be used as an inference tool to conclude that a given semi-Markov process cannot result from coarse graining an underlying Markov one. We illustrate these results with representative examples.
Collapse
Affiliation(s)
- Benjamin Ertel
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jann van der Meer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
26
|
Hasegawa Y. Thermodynamic uncertainty relation for quantum first-passage processes. Phys Rev E 2022; 105:044127. [PMID: 35590682 DOI: 10.1103/physreve.105.044127] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 04/05/2022] [Indexed: 06/15/2023]
Abstract
We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains. We consider first passage processes that stop after a fixed number of jump events, which contrasts with typical quantum Markov chains which end at a fixed time. We obtain bounds for the observables of the first passage processes in quantum Markov chains by the Loschmidt echo, which quantifies the extent of irreversibility in quantum many-body systems. Considering a particular case, we show that the lower bound corresponds to the quantum Fisher information, which plays a fundamental role in uncertainty relations in quantum systems. Moreover, considering classical dynamics, our bound reduces to a thermodynamic uncertainty relation for classical first passage processes.
Collapse
Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
27
|
Falasco G, Barkai E, Baiesi M. Generalized virial equation for nonlinear multiplicative Langevin dynamics: Application to laser-cooled atoms. Phys Rev E 2022; 105:024143. [PMID: 35291090 DOI: 10.1103/physreve.105.024143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Accepted: 02/10/2022] [Indexed: 06/14/2023]
Abstract
The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize it for confined laser-cooled atoms in the semiclassical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semiclassical regime.
Collapse
Affiliation(s)
- Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Eli Barkai
- Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel
| | - Marco Baiesi
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| |
Collapse
|
28
|
Gao Q, Chun HM, Horowitz JM. Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions. Phys Rev E 2022; 105:L012102. [PMID: 35193184 DOI: 10.1103/physreve.105.l012102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 12/21/2021] [Indexed: 11/07/2022]
Abstract
We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.
Collapse
Affiliation(s)
- Qi Gao
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Hyun-Myung Chun
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Jordan M Horowitz
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.,Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA.,Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
| |
Collapse
|
29
|
Hasegawa Y. Irreversibility, Loschmidt Echo, and Thermodynamic Uncertainty Relation. PHYSICAL REVIEW LETTERS 2021; 127:240602. [PMID: 34951787 DOI: 10.1103/physrevlett.127.240602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 10/28/2021] [Indexed: 06/14/2023]
Abstract
Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by the Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed dynamics, our relation leads to several thermodynamic uncertainty relations, indicating that our relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.
Collapse
Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
30
|
Pietzonka P, Guioth J, Jack RL. Cycle counts and affinities in stochastic models of nonequilibrium systems. Phys Rev E 2021; 104:064137. [PMID: 35030867 DOI: 10.1103/physreve.104.064137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 12/08/2021] [Indexed: 06/14/2023]
Abstract
For nonequilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any given cycle is described by universal formulas which depend on the cycle affinity, but are otherwise independent of system details. We discuss the similarities and differences of this result to fluctuation theorems, and generalize the result to families of cycles, relevant under coarse graining. Finally, we describe the application of large deviation theory to this cycle-counting problem.
Collapse
Affiliation(s)
- Patrick Pietzonka
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Jules Guioth
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Univ. Lyon, ÉNS de Lyon, Univ. Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
31
|
Kamijima T, Otsubo S, Ashida Y, Sagawa T. Higher-order efficiency bound and its application to nonlinear nanothermoelectrics. Phys Rev E 2021; 104:044115. [PMID: 34781477 DOI: 10.1103/physreve.104.044115] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Accepted: 09/22/2021] [Indexed: 11/07/2022]
Abstract
Power and efficiency of heat engines are two conflicting objectives. A tight efficiency bound is expected to give insights on the fundamental properties of such a power-efficiency tradeoff. Here, we derive an upper bound on the efficiency of steady-state heat engines, which incorporates higher-order fluctuations of power. In a prototypical model of nonlinear nanostructured thermoelectrics, we show that the obtained bound is tighter than a well-established efficiency bound derived from the thermodynamic uncertainty relation, demonstrating that the higher-order terms have rich information about the thermodynamic efficiency in the nonlinear regime. In particular, we find that the higher-order bound is exactly achieved if the tight coupling condition is satisfied. The obtained bound gives a consistent prediction with an observation that nonlinearity enhances the power-efficiency tradeoff, and would also be useful in a variety of nanoscale engines.
Collapse
Affiliation(s)
- Takuya Kamijima
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Shun Otsubo
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Yuto Ashida
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.,Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.,Quantum-Phase Electronics Center (QPEC), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|
32
|
Van Vu T, Hasegawa Y. Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2021; 127:190601. [PMID: 34797124 DOI: 10.1103/physrevlett.127.190601] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 10/04/2021] [Indexed: 06/13/2023]
Abstract
We consider the thermal relaxation process of a quantum system attached to single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower bounded by a relative entropy between the unitarily evolved state and the final state. The bound characterizes the state discrepancy induced by the nonunitary dynamics, and thus reflects the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian, thereby providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. This finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.
Collapse
Affiliation(s)
- Tan Van Vu
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
33
|
Hartich D, Godec A. Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion. PHYSICAL REVIEW LETTERS 2021; 127:080601. [PMID: 34477441 DOI: 10.1103/physrevlett.127.080601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.
Collapse
Affiliation(s)
- David Hartich
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
| |
Collapse
|
34
|
Song Y, Hyeon C. Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation. eLife 2021; 10:70034. [PMID: 34402427 PMCID: PMC8457829 DOI: 10.7554/elife.70034] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Accepted: 08/13/2021] [Indexed: 01/05/2023] Open
Abstract
Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal λ. Our finding underscores the cost-effectiveness of precise morphogen profile formation in Drosophila development.
Collapse
Affiliation(s)
- Yonghyun Song
- Korea Institute for Advanced Study, Seoul, Republic of Korea
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul, Republic of Korea
| |
Collapse
|
35
|
Lesnicki D, Gao CY, Limmer DT, Rotenberg B. On the molecular correlations that result in field-dependent conductivities in electrolyte solutions. J Chem Phys 2021; 155:014507. [PMID: 34241409 DOI: 10.1063/5.0052860] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Employing recent advances in response theory and nonequilibrium ensemble reweighting, we study the dynamic and static correlations that give rise to an electric field-dependent ionic conductivity in electrolyte solutions. We consider solutions modeled with both implicit and explicit solvents, with different dielectric properties, and at multiple concentrations. Implicit solvent models at low concentrations and small dielectric constants exhibit strongly field-dependent conductivities. We compare these results to Onsager-Wilson theory of the Wien effect, which provides a qualitatively consistent prediction at low concentrations and high static dielectric constants but is inconsistent away from these regimes. The origin of the discrepancy is found to be increased ion correlations under these conditions. Explicit solvent effects act to suppress nonlinear responses, yielding a weakly field-dependent conductivity over the range of physically realizable field strengths. By decomposing the relevant time correlation functions, we find that the insensitivity of the conductivity to the field results from the persistent frictional forces on the ions from the solvent. Our findings illustrate the utility of nonequilibrium response theory in rationalizing nonlinear transport behavior.
Collapse
Affiliation(s)
- Dominika Lesnicki
- Sorbonne Université, CNRS, Physico-Chimie des Electrolytes et Nanosystèmes Interfaciaux, Paris, France
| | - Chloe Y Gao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-Chimie des Electrolytes et Nanosystèmes Interfaciaux, Paris, France
| |
Collapse
|
36
|
Hiura K, Sasa SI. Kinetic uncertainty relation on first-passage time for accumulated current. Phys Rev E 2021; 103:L050103. [PMID: 34134276 DOI: 10.1103/physreve.103.l050103] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Accepted: 05/04/2021] [Indexed: 11/07/2022]
Abstract
The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this Letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium.
Collapse
Affiliation(s)
- Ken Hiura
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| |
Collapse
|
37
|
Nakayama Y, Toyabe S. Optimal Rectification without Forward-Current Suppression by Biological Molecular Motor. PHYSICAL REVIEW LETTERS 2021; 126:208101. [PMID: 34110213 DOI: 10.1103/physrevlett.126.208101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 04/23/2021] [Indexed: 06/12/2023]
Abstract
We experimentally show that biological molecular motor F_{1}-ATPase (F_{1}) implements an optimal rectification mechanism. The rectification mechanism hardly suppresses the synthesis of adenosine triphosphate by F_{1}, which is F_{1}'s physiological role, while inhibiting the unfavorable hydrolysis of adenosine triphosphate. This optimal rectification contrasts highly with that of a simple ratchet model, where the inhibition of the backward current is inevitably accompanied by the suppression of the forward current. Our detailed analysis of single-molecule trajectories demonstrates a novel but simple rectification mechanism of F_{1} with parallel landscapes and asymmetric transition rates.
Collapse
Affiliation(s)
- Yohei Nakayama
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Aoba 6-6-05, Sendai 980-8579, Japan
| | - Shoichi Toyabe
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Aoba 6-6-05, Sendai 980-8579, Japan
| |
Collapse
|
38
|
Song Y, Hyeon C. Thermodynamic uncertainty relation to assess biological processes. J Chem Phys 2021; 154:130901. [PMID: 33832251 DOI: 10.1063/5.0043671] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product Q of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration is at the Michaelis constant, and some of the key biological processes are found to work around this condition. We illustrate the utility of Q in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes), we discuss how their optimality quantified in terms of Q is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of Q recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.
Collapse
Affiliation(s)
- Yonghyun Song
- Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul 02455, South Korea
| |
Collapse
|
39
|
GrandPre T, Klymko K, Mandadapu KK, Limmer DT. Entropy production fluctuations encode collective behavior in active matter. Phys Rev E 2021; 103:012613. [PMID: 33601608 DOI: 10.1103/physreve.103.012613] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 12/22/2020] [Indexed: 11/07/2022]
Abstract
We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particles. We also derive optimal control forces that realize the dynamics necessary to tune dissipation and manipulate the system between phases. In so doing, we uncover a general relationship between entropy production and pattern formation in active matter, as well as ways of controlling it.
Collapse
Affiliation(s)
- Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94609, USA
| | - Katherine Klymko
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94609, USA.,Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - David T Limmer
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Department of Chemistry, University of California, Berkeley, California 94609, USA.,Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Kavli Energy NanoScience Institute, Berkeley, California 94609, USA
| |
Collapse
|
40
|
Rignon-Bret A, Guarnieri G, Goold J, Mitchison MT. Thermodynamics of precision in quantum nanomachines. Phys Rev E 2021; 103:012133. [PMID: 33601640 DOI: 10.1103/physreve.103.012133] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 12/18/2020] [Indexed: 12/14/2022]
Abstract
Fluctuations strongly affect the dynamics and functionality of nanoscale thermal machines. Recent developments in stochastic thermodynamics have shown that fluctuations in many far-from-equilibrium systems are constrained by the rate of entropy production via so-called thermodynamic uncertainty relations. These relations imply that increasing the reliability or precision of an engine's power output comes at a greater thermodynamic cost. Here we study the thermodynamics of precision for small thermal machines in the quantum regime. In particular, we derive exact relations between the power, power fluctuations, and entropy production rate for several models of few-qubit engines (both autonomous and cyclic) that perform work on a quantized load. Depending on the context, we find that quantum coherence can either help or hinder where power fluctuations are concerned. We discuss design principles for reducing such fluctuations in quantum nanomachines and propose an autonomous three-qubit engine whose power output for a given entropy production is more reliable than would be allowed by any classical Markovian model.
Collapse
Affiliation(s)
- Antoine Rignon-Bret
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland.,École Normale Supérieure, 45 rue d'Ulm, F-75230 Paris, France
| | - Giacomo Guarnieri
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Mark T Mitchison
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| |
Collapse
|
41
|
Vo VT, Van Vu T, Hasegawa Y. Unified approach to classical speed limit and thermodynamic uncertainty relation. Phys Rev E 2021; 102:062132. [PMID: 33465987 DOI: 10.1103/physreve.102.062132] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Accepted: 11/19/2020] [Indexed: 01/15/2023]
Abstract
The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano-Sasa entropy production. Notably, the obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.
Collapse
Affiliation(s)
- Van Tuan Vo
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Tan Van Vu
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
42
|
Hasegawa Y. Thermodynamic Uncertainty Relation for General Open Quantum Systems. PHYSICAL REVIEW LETTERS 2021; 126:010602. [PMID: 33480784 DOI: 10.1103/physrevlett.126.010602] [Citation(s) in RCA: 29] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Accepted: 11/30/2020] [Indexed: 06/12/2023]
Abstract
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the system-environment interaction, we bound the counting observables in the environment by the survival activity, which reduces to the dynamical activity in classical Markov processes. Remarkably, the relation derived herein holds for general open quantum systems with any counting observable and any initial state. Therefore, our relation is satisfied for classical Markov processes with arbitrary time-dependent transition rates and initial states. We apply our relation to continuous measurement and the quantum walk to find that the quantum nature of the system can enhance the precision. Moreover, we can make the lower bound arbitrarily small by employing appropriate continuous measurement.
Collapse
Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
43
|
Koyuk T, Seifert U. Thermodynamic Uncertainty Relation for Time-Dependent Driving. PHYSICAL REVIEW LETTERS 2020; 125:260604. [PMID: 33449796 DOI: 10.1103/physrevlett.125.260604] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Accepted: 12/09/2020] [Indexed: 05/10/2023]
Abstract
Thermodynamic uncertainty relations yield a lower bound on entropy production in terms of the mean and fluctuations of a current. We derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states and extend these relations beyond currents to state variables. The quality of the bound is discussed for various types of observables for an interacting pair of colloidal particles in a moving laser trap and for the dynamical unfolding of a small protein. Since the input for evaluating these bounds does not require specific knowledge of the system or its coupling to the time-dependent control, they should become widely applicable tools for thermodynamic inference in time-dependently driven systems.
Collapse
Affiliation(s)
- Timur Koyuk
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
44
|
Wang Y. Sub-Gaussian and subexponential fluctuation-response inequalities. Phys Rev E 2020; 102:052105. [PMID: 33327146 DOI: 10.1103/physreve.102.052105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2020] [Accepted: 10/12/2020] [Indexed: 11/07/2022]
Abstract
Sub-Gaussian and subexponential distributions are introduced and applied to study the fluctuation-response relation out of equilibrium. A bound on the difference in expected values of an arbitrary sub-Gaussian or subexponential physical quantity is established in terms of its sub-Gaussian or subexponential norm. Based on that, we find that the entropy difference between two states is bounded by the energy fluctuation in these states. Moreover, we obtain generalized versions of the thermodynamic uncertainty relation in different regimes. Operational issues concerning the application of our results in an experimental setting are also addressed, and nonasymptotic bounds on the errors incurred by using the sample mean instead of the expected value in our fluctuation-response inequalities are derived.
Collapse
Affiliation(s)
- Yan Wang
- Department of Statistics, Iowa State University, Ames, Iowa 50011, USA
| |
Collapse
|
45
|
Yang C, Wei X, Sheng J, Wu H. Phonon heat transport in cavity-mediated optomechanical nanoresonators. Nat Commun 2020; 11:4656. [PMID: 32938953 PMCID: PMC7494915 DOI: 10.1038/s41467-020-18426-4] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 08/13/2020] [Indexed: 12/03/2022] Open
Abstract
The understanding of heat transport in nonequilibrium thermodynamics is an important research frontier, which is crucial for implementing novel thermodynamic devices, such as heat engines and refrigerators. The convection, conduction, and radiation are the well-known basic ways to transfer thermal energy. Here, we demonstrate a different mechanism of phonon heat transport between two spatially separated nanomechanical resonators coupled by the cavity-enhanced long-range interactions. The single trajectory for thermalization and non-equilibrium dynamics is monitored in real-time. In the strong coupling regime, the instant heat flux spontaneously oscillates back and forth in the nonequilibrium steady states. The universal bound on the precision of nonequilibrium steady-state heat flux, i.e. the thermodynamic uncertainty relation, is verified in such a temperature gradient driven far-off equilibrium system. Our results give more insight into the heat transfer with nanomechanical oscillators, and provide a playground for testing fundamental theories in non-equilibrium thermodynamics. Heat flux is well understood on macroscopic scales, however when the system size is reduced, novel phenomena are induced by fluctuations. Here, the authors demonstrate phonon heat transport between two nanomechanical resonators coupled by cavity enhanced interactions exhibiting an oscillating heat flux.
Collapse
Affiliation(s)
- Cheng Yang
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China
| | - Xinrui Wei
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China
| | - Jiteng Sheng
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China. .,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, 030006, China.
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China. .,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, 030006, China.
| |
Collapse
|
46
|
Ishijima A, Okada Y. Information physics of living matters. Biophys Physicobiol 2020; 17:130-131. [PMID: 33240739 PMCID: PMC7671737 DOI: 10.2142/biophysico.bsj-2020024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 09/07/2020] [Indexed: 12/01/2022] Open
Affiliation(s)
- Akihiko Ishijima
- Graduate School of Frontier Biosciences, Osaka University, Suita, Osaka 565-0871, Japan
| | - Yasushi Okada
- Laboratory for Cell Polarity Regulation, RIKEN Center for Biosystems Dynamics Research (BDR), Suita, Osaka 565-0874, Japan
- Department of Cell Biology, Department of Physics, Universal Biology Institute (UBI), and International Research Center for Neurointelligence (WPI-IRCN), the University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
| |
Collapse
|
47
|
Fischer LP, Chun HM, Seifert U. Free diffusion bounds the precision of currents in underdamped dynamics. Phys Rev E 2020; 102:012120. [PMID: 32794919 DOI: 10.1103/physreve.102.012120] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Accepted: 04/21/2020] [Indexed: 11/07/2022]
Abstract
The putative generalization of the thermodynamic uncertainty relation (TUR) to underdamped dynamics is still an open problem. So far, bounds that have been derived for such a dynamics are not particularly transparent and they do not converge to the known TUR in the overdamped limit. Furthermore, it was found that there are restrictions for a TUR to hold such as the absence of a magnetic field. In this article we first analyze the properties of driven free diffusion in the underdamped regime and show that it inherently violates the overdamped TUR for finite times. Based on numerical evidence, we then conjecture a bound for one-dimensional driven diffusion in a potential which is based on the result for free diffusion. This bound converges to the known overdamped TUR in the corresponding limit. Moreover, the conjectured bound holds for observables that involve higher powers of the velocity as long as the observable is odd under time reversal. Finally, we address the applicability of this bound to underdamped dynamics in higher dimensions.
Collapse
Affiliation(s)
- Lukas P Fischer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Hyun-Myung Chun
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
48
|
Hasegawa Y. Quantum Thermodynamic Uncertainty Relation for Continuous Measurement. PHYSICAL REVIEW LETTERS 2020; 125:050601. [PMID: 32794846 DOI: 10.1103/physrevlett.125.050601] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 07/01/2020] [Indexed: 06/11/2023]
Abstract
We use quantum estimation theory to derive a thermodynamic uncertainty relation in Markovian open quantum systems, which bounds the fluctuation of continuous measurements. The derived quantum thermodynamic uncertainty relation holds for arbitrary continuous measurements satisfying a scaling condition. We derive two relations; the first relation bounds the fluctuation by the dynamical activity and the second one does so by the entropy production. We apply our bounds to a two-level atom driven by a laser field and a three-level quantum thermal machine with jump and diffusion measurements. Our result shows that there exists a universal bound upon the fluctuations, regardless of continuous measurements.
Collapse
Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| |
Collapse
|
49
|
Otsubo S, Ito S, Dechant A, Sagawa T. Estimating entropy production by machine learning of short-time fluctuating currents. Phys Rev E 2020; 101:062106. [PMID: 32688599 DOI: 10.1103/physreve.101.062106] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 05/05/2020] [Indexed: 11/07/2022]
Abstract
Thermodynamic uncertainty relations (TURs) are the inequalities which give lower bounds on the entropy production rate using only the mean and the variance of fluctuating currents. Since the TURs do not refer to the full details of the stochastic dynamics, it would be promising to apply the TURs for estimating the entropy production rate from a limited set of trajectory data corresponding to the dynamics. Here we investigate a theoretical framework for estimation of the entropy production rate using the TURs along with machine learning techniques without prior knowledge of the parameters of the stochastic dynamics. Specifically, we derive a TUR for the short-time region and prove that it can provide the exact value, not only a lower bound, of the entropy production rate for Langevin dynamics, if the observed current is optimally chosen. This formulation naturally includes a generalization of the TURs with the partial entropy production of subsystems under autonomous interaction, which reveals the hierarchical structure of the estimation. We then construct estimators on the basis of the short-time TUR and machine learning techniques such as the gradient ascent. By performing numerical experiments, we demonstrate that our learning protocol performs well even in nonlinear Langevin dynamics. We also discuss the case of Markov jump processes, where the exact estimation is shown to be impossible in general. Our result provides a platform that can be applied to a broad class of stochastic dynamics out of equilibrium, including biological systems.
Collapse
Affiliation(s)
- Shun Otsubo
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Sosuke Ito
- Universal Biology Institute, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0031, Japan.,JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
| | - Andreas Dechant
- WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|