1
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Pietzonka P, Coghi F. Thermodynamic cost for precision of general counting observables. Phys Rev E 2024; 109:064128. [PMID: 39020906 DOI: 10.1103/physreve.109.064128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 05/13/2024] [Indexed: 07/20/2024]
Abstract
We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.
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2
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Delvenne JC, Falasco G. Thermokinetic relations. Phys Rev E 2024; 109:014109. [PMID: 38366524 DOI: 10.1103/physreve.109.014109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 11/30/2023] [Indexed: 02/18/2024]
Abstract
Thermokinetic relations bound thermodynamic quantities, such as entropy production of a physical system over a certain time interval, with statistics of kinetic (or dynamical) observables, such as mean total variation of the observable over the time interval. We introduce a thermokinetic relation to bound the entropy production or the nonadiabatic (or excess) entropy production for overdamped Markov jump processes, possibly with time-varying rates and nonstationary distributions. For stationary cases, this bound is akin to a thermodynamic uncertainty relation, only involving absolute fluctuations rather than the mean square, thereby offering a better lower bound far from equilibrium. For nonstationary cases, this bound generalizes (classical) speed limits, where the kinetic term is not necessarily the activity (number of jumps) but any trajectory observable of interest. As a consequence, in the task of driving a system from a given probability distribution to another, we find a tradeoff between nonadiabatic entropy production and housekeeping entropy production: the latter can be increased to decrease the former, although to a limited extent. We also find constraints specific to constant-rate Markov processes. We illustrate our thermokinetic relations on simple examples from biophysics and computing devices.
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Affiliation(s)
- Jean-Charles Delvenne
- Institute of Information and Communication Technologies, Electronics and Applied Mathematics, UCLouvain, 1348 Louvain-La-Neuve, Belgium
| | - Gianmaria Falasco
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
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3
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Bebon R, Godec A. Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime. PHYSICAL REVIEW LETTERS 2023; 131:237101. [PMID: 38134782 DOI: 10.1103/physrevlett.131.237101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Revised: 10/18/2023] [Accepted: 10/31/2023] [Indexed: 12/24/2023]
Abstract
We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.
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Affiliation(s)
- Rick Bebon
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
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4
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Liang S, Pigolotti S. Thermodynamic bounds on time-reversal asymmetry. Phys Rev E 2023; 108:L062101. [PMID: 38243435 DOI: 10.1103/physreve.108.l062101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 11/14/2023] [Indexed: 01/21/2024]
Abstract
Quantifying irreversibility of a system using finite information constitutes a major challenge in stochastic thermodynamics. We introduce an observable that measures the time-reversal asymmetry between two states after a given time lag. Our central result is a bound on the time-reversal asymmetry in terms of the total cycle affinity driving the system out of equilibrium. This result leads to further thermodynamic bounds on the asymmetry of directed fluxes, on the asymmetry of finite-time cross-correlations, and on the cycle affinity of coarse-grained dynamics.
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Affiliation(s)
- Shiling Liang
- Institute of Physics, School of Basic Sciences, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
- Biological Complexity Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Simone Pigolotti
- Biological Complexity Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
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5
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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.
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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
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6
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Tasnim F, Wolpert DH. Stochastic Thermodynamics of Multiple Co-Evolving Systems-Beyond Multipartite Processes. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1078. [PMID: 37510025 PMCID: PMC10378096 DOI: 10.3390/e25071078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 07/14/2023] [Accepted: 07/14/2023] [Indexed: 07/30/2023]
Abstract
Many dynamical systems consist of multiple, co-evolving subsystems (i.e., they have multiple degrees of freedom). Often, the dynamics of one or more of these subsystems will not directly depend on the state of some other subsystems, resulting in a network of dependencies governing the dynamics. How does this dependency network affect the full system's thermodynamics? Prior studies on the stochastic thermodynamics of multipartite processes have addressed this question by assuming that, in addition to the constraints of the dependency network, only one subsystem is allowed to change state at a time. However, in many real systems, such as chemical reaction networks or electronic circuits, multiple subsystems can-or must-change state together. Here, we investigate the thermodynamics of such composite processes, in which multiple subsystems are allowed to change state simultaneously. We first present new, strictly positive lower bounds on entropy production in composite processes. We then present thermodynamic uncertainty relations for information flows in composite processes. We end with strengthened speed limits for composite processes.
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Affiliation(s)
- Farita Tasnim
- Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - David H Wolpert
- Santa Fe Institute, Santa Fe, NM 87501, USA
- Complexity Science Hub, Josefstadter Straße 39, 1080 Vienna, Austria
- Center for Bio-Social Complex Systems, Arizona State University, Tempe, AZ 85287, USA
- International Center for Theoretical Physics, 34151 Trieste, Italy
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7
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Cao Z, Bao R, Hou Z. Cascade-enhanced transport efficiency of biochemical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:2894486. [PMID: 37276569 DOI: 10.1063/5.0146769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 05/08/2023] [Indexed: 06/07/2023]
Abstract
Recent developments in nonequilibrium thermodynamics, known as thermodynamic uncertainty relations, limit the system's accuracy by the amount of free-energy consumption. A transport efficiency, which can be used to characterize the capacity to control the fluctuation by means of energy cost, is a direct result of the thermodynamic uncertainty relation. According to our previous research, biochemical systems consume much lower energy cost by noise-induced oscillations to keep almost equal efficiency to maintain precise processes than that by normal oscillations. Here, we demonstrate that the performance of noise-induced oscillations propagating can be further improved through a cascade reaction mechanism. It has been discovered that it is possible to considerably enhance the transport efficiency of the biochemical reactions attained at the terminal cell, allowing the cell to use the cascade reaction mechanism to operate more precisely and efficiently. Moreover, an optimal reaction coupling strength has been predicted to maximize the transport efficiency of the terminal cell, uncovering a concrete design strategy for biochemical systems. By using the local mean field approximation, we have presented an analytical framework by extending the stochastic normal form equation to the system perturbed by external signals, providing an explanation of the optimal coupling strength.
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Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ruicheng Bao
- Department of Chemical Physics and 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 and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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8
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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.
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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
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9
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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.
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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
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10
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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: 3] [Impact Index Per Article: 1.5] [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.
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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
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11
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Dieball C, Godec A. Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space. PHYSICAL REVIEW LETTERS 2022; 129:140601. [PMID: 36240401 DOI: 10.1103/physrevlett.129.140601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 07/19/2022] [Accepted: 07/28/2022] [Indexed: 06/16/2023]
Abstract
We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or nonequilibrium steady states on all timescales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all timescales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.
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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
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12
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Wolpert DH. Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200428. [PMID: 35599569 PMCID: PMC9125225 DOI: 10.1098/rsta.2020.0428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of a priori constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly, the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- David H. Wolpert
- Santa Fe Institute, Santa Fe, NM, USA
- Complexity Science Hub, Vienna, Arizona State University, Tempe, AZ, USA
- International Center for Theoretical Physics, Italy
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13
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Wolpert DH. Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022. [PMID: 35599569 DOI: 10.6084/m9.figshare.c.5896494] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of a priori constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly, the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- David H Wolpert
- Santa Fe Institute, Santa Fe, NM, USA
- Complexity Science Hub, Vienna, Arizona State University, Tempe, AZ, USA
- International Center for Theoretical Physics, Italy
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14
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Verification of Information Thermodynamics in a Trapped Ion System. ENTROPY 2022; 24:e24060813. [PMID: 35741534 PMCID: PMC9222944 DOI: 10.3390/e24060813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Revised: 06/07/2022] [Accepted: 06/08/2022] [Indexed: 02/05/2023]
Abstract
Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.
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15
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Van Vu T, Saito K. Thermodynamics of Precision in Markovian Open Quantum Dynamics. PHYSICAL REVIEW LETTERS 2022; 128:140602. [PMID: 35476476 DOI: 10.1103/physrevlett.128.140602] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2021] [Revised: 03/02/2022] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.
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Affiliation(s)
- Tan Van Vu
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - Keiji Saito
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
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16
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Yan LL, Zhang JW, Yun MR, Li JC, Ding GY, Wei JF, Bu JT, Wang B, Chen L, Su SL, Zhou F, Jia Y, Liang EJ, Feng M. Experimental Verification of Dissipation-Time Uncertainty Relation. PHYSICAL REVIEW LETTERS 2022; 128:050603. [PMID: 35179926 DOI: 10.1103/physrevlett.128.050603] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Revised: 11/08/2021] [Accepted: 01/14/2022] [Indexed: 06/14/2023]
Abstract
Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.
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Affiliation(s)
- L-L Yan
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - J-W Zhang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
| | - M-R Yun
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - J-C Li
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - G-Y Ding
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - J-F Wei
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - J-T Bu
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - B Wang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - L Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
| | - S-L Su
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - F Zhou
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
| | - Y Jia
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
- Key Laboratory for Special Functional Materials of Ministry of Education, and School of Materials and Engineering, Henan University, Kaifeng 475001, China
| | - E-J Liang
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - M Feng
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
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17
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Kolchinsky A, Wolpert DH. Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes. Phys Rev E 2021; 104:054107. [PMID: 34942730 DOI: 10.1103/physreve.104.054107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 09/28/2021] [Indexed: 11/07/2022]
Abstract
We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state ρ, above the minimum EP incurred by the same process on any initial state. We show that this additional EP, which we term the "mismatch cost of ρ," has a universal information-theoretic form: it is given by the contraction of the relative entropy between ρ and the least-dissipative initial state φ over time. We derive versions of this result for integrated EP incurred over the course of a process, for trajectory-level fluctuating EP, and for instantaneous EP rate. We also show that mismatch cost for fluctuating EP obeys an integral fluctuation theorem. Our results demonstrate a fundamental relationship between thermodynamic irreversibility (generation of EP) and logical irreversibility (inability to know the initial state corresponding to a given final state). We use this relationship to derive quantitative bounds on the thermodynamics of quantum error correction and to propose a thermodynamically operationalized measure of the logical irreversibility of a quantum channel. Our results hold for both finite- and infinite-dimensional systems, and generalize beyond EP to many other thermodynamic costs, including nonadiabatic EP, free-energy loss, and entropy gain.
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Affiliation(s)
- Artemy Kolchinsky
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
| | - David H Wolpert
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
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18
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Shpielberg O, Pal A. Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies. Phys Rev E 2021; 104:064141. [PMID: 35030838 DOI: 10.1103/physreve.104.064141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 12/02/2021] [Indexed: 06/14/2023]
Abstract
A universal large N theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse-grained thermodynamic uncertainty relations-one of them being an activity bound. Importantly, the activity serves as a tighter bound for the entropy production in 1D systems. These results are particularly useful in the many-body regime, where typically a coarse-grained approach is required to handle the large microscopic state space.
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Affiliation(s)
- Ohad Shpielberg
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Mt. Carmel, Haifa 31905, Israel
| | - Arnab Pal
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University & Department of Physics, Indian Institute of Technology, Kanpur, Kanpur 208016, India
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19
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Pigolotti S. Generalized Euler-Lotka equation for correlated cell divisions. Phys Rev E 2021; 103:L060402. [PMID: 34271641 DOI: 10.1103/physreve.103.l060402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 04/27/2021] [Indexed: 11/07/2022]
Abstract
Cell division times in microbial populations display significant fluctuations that impact the population growth rate in a nontrivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical biology. However, cell division times can be significantly correlated, due to physical properties of cells that are passed through generations. In this Letter, we derive an equation remarkably similar to the Euler-Lotka equation which is valid in the presence of correlations. Our exact result is based on large deviation theory and does not require particularly strong assumptions on the underlying dynamics. We apply our theory to a phenomenological model of bacterial cell division in E. coli and to experimental data. We find that the discrepancy between the growth rate predicted by the Euler-Lotka equation and our generalized version is relatively small, but large enough to be measurable by our approach.
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Affiliation(s)
- Simone Pigolotti
- Biological Complexity Unit, Okinawa Institute of Science and Technology and Graduate University, Onna, Okinawa 904-0495, Japan
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20
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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.
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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
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21
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Abstract
Temporal order in living matters reflects the self-organizing nature of dynamical processes driven out of thermodynamic equilibrium. Because of functional reasons, the period of a biochemical oscillation must be tuned to a specific value with precision; however, according to the thermodynamic uncertainty relation (TUR), the precision of the oscillatory period is constrained by the thermodynamic cost of generating it. After reviewing the basics of chemical oscillations using the Brusselator as a model system, we study the glycolytic oscillation generated by octameric phosphofructokinase (PFK), which is known to display a period of several minutes. By exploring the phase space of glycolytic oscillations, we find that the glycolytic oscillation under the cellular condition is realized in a cost-effective manner. Specifically, over the biologically relevant range of parameter values of glycolysis and octameric PFK, the entropy production from the glycolytic oscillation is minimal when the oscillation period is (5-10) min. Furthermore, the glycolytic oscillation is found at work near the phase boundary of limit cycles, suggesting that a moderate increase of glucose injection rate leads to the loss of oscillatory dynamics, which is reminiscent of the loss of pulsatile insulin release resulting from elevated blood glucose level.
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Affiliation(s)
- Pureun Kim
- Korea Institute for Advanced Study, Seoul 02455, Korea
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22
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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.
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Affiliation(s)
- Yonghyun Song
- Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul 02455, South Korea
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23
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Saryal S, Sadekar O, Agarwalla BK. Thermodynamic uncertainty relation for energy transport in a transient regime: A model study. Phys Rev E 2021; 103:022141. [PMID: 33736118 DOI: 10.1103/physreve.103.022141] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
We investigate a transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production. We explore this relation in the context of energy transport in a bipartite setting for three exactly solvable toy model systems (two coupled harmonic oscillators, two coupled qubits, and a hybrid coupled oscillator-qubit system) and analyze the role played by the underlying statistics of the transport carriers in the TUR. Interestingly, for all these models, depending on the statistics, the TUR ratio can be expressed as a sum or a difference of a universal term which is always greater than or equal to 2 and a corresponding entropy production term. We find that the generalized version of the TUR, originating from the universal fluctuation symmetry, is always satisfied. However, interestingly, the specialized TUR, a tighter bound, is always satisfied for the coupled harmonic oscillator system obeying Bose-Einstein statistics. Whereas, for both the coupled qubit, obeying Fermi-like statistics, and the hybrid qubit-oscillator system with mixed Fermi-Bose statistics, violation of the tighter bound is observed in certain parameter regimes. We have provided conditions for such violations. We also provide a rigorous proof following the nonequilibrium Green's function approach that the tighter bound is always satisfied in the weak-coupling regime for generic bipartite systems.
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Affiliation(s)
- Sushant Saryal
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Onkar Sadekar
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
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24
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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: 44] [Impact Index Per Article: 11.0] [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.
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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
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25
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Falasco G, Esposito M. Dissipation-Time Uncertainty Relation. PHYSICAL REVIEW LETTERS 2020; 125:120604. [PMID: 33016734 DOI: 10.1103/physrevlett.125.120604] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2020] [Accepted: 08/14/2020] [Indexed: 05/10/2023]
Abstract
We show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff ⟨S[over ˙]_{e}⟩T≥k_{B} between the entropy flow ⟨S[over ˙]_{e}⟩ into the reservoirs and the mean time T to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.
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Affiliation(s)
- Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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26
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Marsland R, Cui W, Horowitz JM. The thermodynamic uncertainty relation in biochemical oscillations. J R Soc Interface 2020; 16:20190098. [PMID: 31039695 DOI: 10.1098/rsif.2019.0098] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Living systems regulate many aspects of their behaviour through periodic oscillations of molecular concentrations, which function as 'biochemical clocks.' The chemical reactions that drive these clocks are intrinsically stochastic at the molecular level, so that the duration of a full oscillation cycle is subject to random fluctuations. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy budget, the recently discovered 'thermodynamic uncertainty relation' yields the magnitude of period fluctuations in the most precise conceivable free-running clock. In this paper, we show that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum. We argue that this suboptimal performance is due to the small number of internal states per molecule in these models, combined with the high level of thermodynamic force required to maintain the system in the oscillatory phase. We introduce a new model with a tunable number of internal states per molecule and confirm that it approaches the optimal precision as this number increases.
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Affiliation(s)
- Robert Marsland
- 1 Department of Physics, Boston University , 590 Commonwealth Avenue, Boston, MA 02215 , USA
| | - Wenping Cui
- 1 Department of Physics, Boston University , 590 Commonwealth Avenue, Boston, MA 02215 , USA.,2 Department of Physics, Boston College , 140 Commonwealth Avenue, Chestnut Hill, MA 02467 , USA
| | - Jordan M Horowitz
- 3 Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square , Cambridge, MA 02139 , USA.,4 Department of Biophysics, University of Michigan , Ann Arbor, MI 48109 , USA.,5 Center for the Study of Complex Systems, University of Michigan , Ann Arbor, MI 48109 , USA
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27
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Neri I. Second Law of Thermodynamics at Stopping Times. PHYSICAL REVIEW LETTERS 2020; 124:040601. [PMID: 32058768 DOI: 10.1103/physrevlett.124.040601] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Indexed: 06/10/2023]
Abstract
Events in mesoscopic systems often take place at first-passage times, as is for instance the case for a colloidal particle that escapes a metastable state. An interesting question is how much work an external agent has done on a particle when it escapes a metastable state. We develop a thermodynamic theory for processes in mesoscopic systems that terminate at stopping times, which generalize first-passage times. This theory implies a thermodynamic bound, reminiscent of the second law of thermodynamics, for the work exerted by an external protocol on a mesoscopic system at a stopping time. As an illustration, we use this law to bound the work required to stretch a polymer to a certain length or to let a particle escape from a metastable state.
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Affiliation(s)
- Izaak Neri
- Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom
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28
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Zhang D, Cao Y, Ouyang Q, Tu Y. The energy cost and optimal design for synchronization of coupled molecular oscillators. NATURE PHYSICS 2020; 16:95-100. [PMID: 32670386 PMCID: PMC7363412 DOI: 10.1038/s41567-019-0701-7] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Accepted: 09/23/2019] [Indexed: 05/24/2023]
Abstract
A model of coupled molecular biochemical oscillators is proposed to study nonequilibrium thermodynamics of synchronization. We find that synchronization of nonequilibrium oscillators costs addition energy to drive the exchange reaction (chemical interaction) between individual oscillators. By solving the steady state of the many-body system analytically, we show that the system goes through a nonequilibrium phase transition driven by energy dissipation, and the critical energy dissipation depends on both the frequency and strength of the exchange reaction. Moreover, our study reveals the optimal design for achieving maximum synchronization with a fixed energy budget. We apply our general theory to the Kai system in Cyanobacteria circadian clock and predict a relationship between the KaiC ATPase activity and synchronization of the KaiC hexamers. The theoretical framework can be extended to study thermodynamics of collective behaviors in other extended nonequilibrium active systems.
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Affiliation(s)
- Dongliang Zhang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Yuansheng Cao
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Qi Ouyang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, AAIC, Peking University, Beijing 100871, China
| | - Yuhai Tu
- IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
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29
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Jacobson D, Whitelam S. Direct evaluation of dynamical large-deviation rate functions using a variational ansatz. Phys Rev E 2019; 100:052139. [PMID: 31869879 DOI: 10.1103/physreve.100.052139] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2019] [Indexed: 06/10/2023]
Abstract
We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a time-extensive dynamical observable. We construct a reference model, a variational ansatz for the behavior of the original model conditioned on atypical values of the observable. Direct simulation of the reference model provides an upper bound on the large-deviation rate function associated with the original model, an estimate of the tightness of the bound, and, if the ansatz is chosen well, the exact rate function. The exact rare behavior of the original model does not need to be known in advance. We use this method to calculate rate functions for currents and counting observables in a set of network- and lattice models taken from the literature. Straightforward ansätze yield bounds that are tighter than bounds obtained from Level 2.5 of large deviations via approximations that involve uniform scalings of rates. We show how to correct these bounds in order to recover the rate functions exactly. Our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations.
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Affiliation(s)
- Daniel Jacobson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
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30
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Van Vu T, Hasegawa Y. Uncertainty relations for underdamped Langevin dynamics. Phys Rev E 2019; 100:032130. [PMID: 31640023 DOI: 10.1103/physreve.100.032130] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Indexed: 11/07/2022]
Abstract
A trade-off between the precision of an arbitrary current and the dissipation, known as the thermodynamic uncertainty relation, has been investigated for various Markovian systems. Here, we study the thermodynamic uncertainty relation for underdamped Langevin dynamics. By employing information inequalities, we prove that for such systems, the relative fluctuation of a current at a steady state is constrained by both the entropy production and the average dynamical activity. We find that unlike what is the case for overdamped dynamics, the dynamical activity plays an important role in the bound. We illustrate our results with two systems, a single-well potential system and a periodically driven Brownian particle model, and numerically verify the inequalities.
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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
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31
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Yan J, Hilfinger A, Vinnicombe G, Paulsson J. Kinetic Uncertainty Relations for the Control of Stochastic Reaction Networks. PHYSICAL REVIEW LETTERS 2019; 123:108101. [PMID: 31573304 DOI: 10.1103/physrevlett.123.108101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2019] [Revised: 06/27/2019] [Indexed: 06/10/2023]
Abstract
Nonequilibrium stochastic reaction networks are commonly found in both biological and nonbiological systems, but have remained hard to analyze because small differences in rate functions or topology can change the dynamics drastically. Here, we conjecture exact quantitative inequalities that relate the extent of fluctuations in connected components, for various network topologies. Specifically, we find that regardless of how two components affect each other's production rates, it is impossible to suppress fluctuations below the uncontrolled equivalents for both components: one must increase its fluctuations for the other to be suppressed. For systems in which components control each other in ringlike structures, it appears that fluctuations can only be suppressed in one component if all other components instead increase fluctuations, compared to the case without control. Even the general N-component system-with arbitrary connections and parameters-must have at least one component with increased fluctuations to reduce fluctuations in others. In connected reaction networks it thus appears impossible to reduce the statistical uncertainty in all components, regardless of the control mechanisms or energy dissipation.
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Affiliation(s)
- Jiawei Yan
- Department of Systems Biology, Harvard University, 200 Longwood Avenue, Boston, Massachusetts 02115, USA
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Andreas Hilfinger
- Department of Chemical & Physical Sciences, University of Toronto, Mississauga, Ontario L5L 1C6, Canada
- Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada
- Department of Cell & Systems Biology, University of Toronto, 25 Harbord Street, Toronto, Ontario M5S 3G5, Canada
| | - Glenn Vinnicombe
- Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
| | - Johan Paulsson
- Department of Systems Biology, Harvard University, 200 Longwood Avenue, Boston, Massachusetts 02115, USA
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32
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Chiuchiú D, Tu Y, Pigolotti S. Error-Speed Correlations in Biopolymer Synthesis. PHYSICAL REVIEW LETTERS 2019; 123:038101. [PMID: 31386470 PMCID: PMC7402413 DOI: 10.1103/physrevlett.123.038101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2019] [Indexed: 06/10/2023]
Abstract
Synthesis of biopolymers such as DNA, RNA, and proteins are biophysical processes aided by enzymes. The performance of these enzymes is usually characterized in terms of their average error rate and speed. However, because of thermal fluctuations in these single-molecule processes, both error and speed are inherently stochastic quantities. In this Letter, we study fluctuations of error and speed in biopolymer synthesis and show that they are in general correlated. This means that, under equal conditions, polymers that are synthesized faster due to a fluctuation tend to have either better or worse errors than the average. The error-correction mechanism implemented by the enzyme determines which of the two cases holds. For example, discrimination in the forward reaction rates tends to grant smaller errors to polymers with faster synthesis. The opposite occurs for discrimination in monomer rejection rates. Our results provide an experimentally feasible way to identify error-correction mechanisms by measuring the error-speed correlations.
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Affiliation(s)
- Davide Chiuchiú
- Biological Complexity Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Yuhai Tu
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Simone Pigolotti
- Biological Complexity Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
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33
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Van Vu T, Hasegawa Y. Uncertainty relations for time-delayed Langevin systems. Phys Rev E 2019; 100:012134. [PMID: 31499914 DOI: 10.1103/physreve.100.012134] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2018] [Indexed: 06/10/2023]
Abstract
The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for non-Markovian systems; therefore, we investigate the thermodynamic uncertainty relation for time-delayed Langevin systems. We prove that the fluctuation of arbitrary dynamical observables is constrained by the Kullback-Leibler divergence between the distributions of the forward path and its reversed counterpart. Specifically, for observables that are antisymmetric under time reversal, the fluctuation is bounded from below by a function of a quantity that can be identified as a generalization of the total entropy production in Markovian systems. We also provide a lower bound for arbitrary observables that are odd under position reversal. The term in this bound reflects the extent to which the position symmetry has been broken in the system and can be positive even in equilibrium. Our results hold for finite observation times and a large class of time-delayed systems because detailed underlying dynamics are not required for the derivation. We numerically verify the derived uncertainty relations using two single time-delay systems and one distributed time-delay system.
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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
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34
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Brown AI, Sivak DA. Pulling cargo increases the precision of molecular motor progress. ACTA ACUST UNITED AC 2019. [DOI: 10.1209/0295-5075/126/40004] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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35
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Koyuk T, Seifert U. Operationally Accessible Bounds on Fluctuations and Entropy Production in Periodically Driven Systems. PHYSICAL REVIEW LETTERS 2019; 122:230601. [PMID: 31298898 DOI: 10.1103/physrevlett.122.230601] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2019] [Indexed: 06/10/2023]
Abstract
For periodically driven systems, we derive a family of inequalities that relate entropy production with experimentally accessible data for the mean, its dependence on driving frequency, and the variance of a large class of observables. With one of these relations, overall entropy production can be bounded by just observing the time spent in a set of states. Among further consequences, the thermodynamic efficiency both of isothermal cyclic engines like molecular motors under a periodic load and of cyclic heat engines can be bounded using experimental data without requiring knowledge of the specific interactions within the system. We illustrate these results for a driven three-level system and for a colloidal Stirling engine.
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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
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36
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Singh S, Menczel P, Golubev DS, Khaymovich IM, Peltonen JT, Flindt C, Saito K, Roldán É, Pekola JP. Universal First-Passage-Time Distribution of Non-Gaussian Currents. PHYSICAL REVIEW LETTERS 2019; 122:230602. [PMID: 31298917 DOI: 10.1103/physrevlett.122.230602] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2018] [Indexed: 06/10/2023]
Abstract
We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of electrons transferred between two metallic islands in the Coulomb blockade regime. Our experimental results are in excellent agreement with numerical calculations based on a recent theory describing the exact first-passage-time distributions for any nonequilibrium stationary Markov process. We also derive a simple analytical approximation for the first-passage-time distribution, which takes into account the non-Gaussian statistics of the electron transport, and show that it describes the experimental distributions with high accuracy. This universal approximation describes a wide class of stochastic processes, and can be used beyond the context of mesoscopic charge transport. In addition, we verify experimentally a fluctuation relation between the first-passage-time distributions for positive and negative thresholds.
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Affiliation(s)
- Shilpi Singh
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Paul Menczel
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Dmitry S Golubev
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Ivan M Khaymovich
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia
| | - Joonas T Peltonen
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Christian Flindt
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Keiji Saito
- Department of Physics, Keio University-Yokohama 2238522, Japan
| | - Édgar Roldán
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy
| | - Jukka P Pekola
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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37
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Liu J, Segal D. Thermodynamic uncertainty relation in quantum thermoelectric junctions. Phys Rev E 2019; 99:062141. [PMID: 31330645 DOI: 10.1103/physreve.99.062141] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2019] [Indexed: 06/10/2023]
Abstract
Recently, a thermodynamic uncertainty relation (TUR) has been formulated for classical Markovian systems demonstrating trade-off between precision (current fluctuation) and cost (dissipation). Systems that violate the TUR are interesting as they overcome another trade-off relation concerning the efficiency of a heat engine, its power, and its stability (power fluctuations). Here, we analyze the root, extent, and impact on performance of TUR violations in quantum thermoelectric junctions at steady state. Considering noninteracting electrons, first we show that only the "classical" component of the current noise, arising from single-electron transfer events, follows the TUR. The remaining, "quantum" part of current noise is therefore responsible for the potential violation of the TUR in such quantum systems. Next, focusing on the resonant transport regime we determine the parameter range in which the violation of the TUR can be observed-for both voltage-biased junctions and thermoelectric engines. We illustrate our findings with exact numerical simulations of a serial double quantum dot system. Most significantly, we demonstrate that the TUR always holds in noninteracting thermoelectric generators when approaching the thermodynamic efficiency limit.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario, Canada M5S 3H6
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario, Canada M5S 3H6
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38
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Macieszczak K, Brandner K, Garrahan JP. Unified Thermodynamic Uncertainty Relations in Linear Response. PHYSICAL REVIEW LETTERS 2018; 121:130601. [PMID: 30312036 DOI: 10.1103/physrevlett.121.130601] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Revised: 08/06/2018] [Indexed: 06/08/2023]
Abstract
Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium processes. Here, we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time-reversal symmetry, including, e.g., ballistic transport and periodically driven classical and quantum systems. We find that, for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics, it reveals a connection between the TUR and current fluctuation theorems.
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Affiliation(s)
- Katarzyna Macieszczak
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Ave., Cambridge CB3 0HE, United Kingdom
| | - Kay Brandner
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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39
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Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 116] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
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Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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40
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Wierenga H, Ten Wolde PR, Becker NB. Quantifying fluctuations in reversible enzymatic cycles and clocks. Phys Rev E 2018; 97:042404. [PMID: 29758603 DOI: 10.1103/physreve.97.042404] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Indexed: 11/07/2022]
Abstract
Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but it also allows fluctuation measurements that may reveal the structure and dynamics of the underlying biochemical network. Here, we study nonequilibrium reaction cycles, such as the mechanochemical cycle of molecular motors, the phosphorylation cycle of circadian clock proteins, or the transition state cycle of enzymes. Fluctuations in such cycles may be measured using either of two classical definitions of the randomness parameter, which we show to be equivalent in general microscopically reversible cycles. We define a stochastic period for reversible cycles and present analytical solutions for its moments. Furthermore, we associate the two forms of the randomness parameter with the thermodynamic uncertainty relation, which sets limits on the timing precision of the cycle in terms of thermodynamic quantities. Our results should prove useful also for the study of temporal fluctuations in more general networks.
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Affiliation(s)
| | | | - Nils B Becker
- DKFZ, Bioquant, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
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41
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Solon AP, Horowitz JM. Phase Transition in Protocols Minimizing Work Fluctuations. PHYSICAL REVIEW LETTERS 2018; 120:180605. [PMID: 29775356 DOI: 10.1103/physrevlett.120.180605] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Indexed: 06/08/2023]
Abstract
For two canonical examples of driven mesoscopic systems-a harmonically trapped Brownian particle and a quantum dot-we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal-work protocols, which therefore never become quasistatic.
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Affiliation(s)
- Alexandre P Solon
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
| | - Jordan M Horowitz
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
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42
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Fischer LP, Pietzonka P, Seifert U. Large deviation function for a driven underdamped particle in a periodic potential. Phys Rev E 2018; 97:022143. [PMID: 29548104 DOI: 10.1103/physreve.97.022143] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2017] [Indexed: 11/07/2022]
Abstract
Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one-dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived, motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.
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Affiliation(s)
- Lukas P Fischer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Patrick Pietzonka
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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43
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Ptaszyński K. First-passage times in renewal and nonrenewal systems. Phys Rev E 2018; 97:012127. [PMID: 29448475 DOI: 10.1103/physreve.97.012127] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Indexed: 11/07/2022]
Abstract
Fluctuations in stochastic systems are usually characterized by full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of the first-passage times, i.e., the time delays after which the counting variable reaches a certain threshold value, is studied. This paper presents the approach to calculate the first-passage time distribution in systems in which the analyzed current is associated with an arbitrary set of transitions within the Markovian network. Using this approach, it is shown that when the subsequent first-passage times are uncorrelated, there exist strict relations between the cumulants of the full counting statistics and the first-passage time distribution. On the other hand, when the correlations of the first-passage times are present, their distribution may provide additional information about the internal dynamics of the system in comparison to the full counting statistics; for example, it may reveal the switching between different dynamical states of the system. Additionally, I show that breaking of the fluctuation theorem for first-passage times may reveal the multicyclic nature of the Markovian network.
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Affiliation(s)
- Krzysztof Ptaszyński
- Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Poznań, Poland
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