1
|
Wu YX, Chen JF, Pei JH, Zhang F, Quan HT. Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold. Phys Rev E 2023; 107:064115. [PMID: 37464632 DOI: 10.1103/physreve.107.064115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Accepted: 05/23/2023] [Indexed: 07/20/2023]
Abstract
The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.
Collapse
Affiliation(s)
- Yu-Xin Wu
- School of Physics, Peking University, Beijing 100871, China
| | - Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China
| | - Ji-Hui Pei
- School of Physics, Peking University, Beijing 100871, China
| | - Fan Zhang
- School of Physics, Peking University, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
| |
Collapse
|
2
|
Chen JF, Quan HT. Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs. Phys Rev E 2023; 107:024135. [PMID: 36932622 DOI: 10.1103/physreve.107.024135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Accepted: 02/09/2023] [Indexed: 06/18/2023]
Abstract
For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint statistics of work and heat in the situation of multiple heat reservoirs via the Feynman-Kac equation. For a classical Brownian particle in contact with multiple heat reservoirs, we verify the validity of the fluctuation theorems for the joint distribution of work and heat.
Collapse
Affiliation(s)
- Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
| |
Collapse
|
3
|
Nickelsen D, Touchette H. Noise correction of large deviations with anomalous scaling. Phys Rev E 2022; 105:064102. [PMID: 35854542 DOI: 10.1103/physreve.105.064102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 05/15/2022] [Indexed: 06/15/2023]
Abstract
We present a path integral calculation of the probability distribution associated with the time-integrated moments of the Ornstein-Uhlenbeck process that includes the Gaussian prefactor in addition to the dominant path or instanton term obtained in the low-noise limit. The instanton term was obtained recently [D. Nickelsen and H. Touchette, Phys. Rev. Lett. 121, 090602 (2018)0031-900710.1103/PhysRevLett.121.090602] and shows that the large deviations of the time-integrated moments are anomalous in the sense that the logarithm of their distribution scales nonlinearly with the integration time. The Gaussian prefactor gives a correction to the low-noise approximation and leads us to define an instanton variance giving some insights as to how anomalous large deviations are created in time. The results are compared with simulations based on importance sampling, extending our previous results based on direct Monte Carlo simulations. We conclude by explaining why many of the standard analytical and numerical methods of large deviation theory fail in the case of anomalous large deviations.
Collapse
Affiliation(s)
- Daniel Nickelsen
- African Institute for Mathematical Sciences (AIMS), Muizenberg 7950, South Africa
| | - Hugo Touchette
- Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa
| |
Collapse
|
4
|
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
|
5
|
Vucelja M, Turitsyn KS, Chertkov M. Extreme-value statistics of work done in stretching a polymer in a gradient flow. Phys Rev E 2015; 91:022123. [PMID: 25768474 DOI: 10.1103/physreve.91.022123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2014] [Indexed: 11/07/2022]
Abstract
We analyze the statistics of work generated by a gradient flow to stretch a nonlinear polymer. We obtain the large deviation function (LDF) of the work in the full range of appropriate parameters by combining analytical and numerical tools. The LDF shows two distinct asymptotes: "near tails" are linear in work and dominated by coiled polymer configurations, while "far tails" are quadratic in work and correspond to preferentially fully stretched polymers. We find the extreme value statistics of work for several singular elastic potentials, as well as the mean and the dispersion of work near the coil-stretch transition. The dispersion shows a maximum at the transition.
Collapse
Affiliation(s)
- M Vucelja
- Center for Studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
| | - K S Turitsyn
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - M Chertkov
- Theory Division & Center for Nonlinear Studies at LANL and with New Mexico Consortium, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
6
|
Lee DY, Kwon C, Pak HK. Nonequilibrium fluctuations for a single-particle analog of gas in a soft wall. PHYSICAL REVIEW LETTERS 2015; 114:060603. [PMID: 25723199 DOI: 10.1103/physrevlett.114.060603] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2014] [Indexed: 06/04/2023]
Abstract
We investigate the motion of a colloidal particle driven out of equilibrium by a time-varying stiffness of the optical trap that produces persistent nonequilibrium work. Measurements of work production for repeated cycles composed of the compression and expansion processes for the optical potential show huge fluctuations due to thermal motion. Using a precise technique to modulate the stiffness in time, we accurately estimate the probability distributions of work produced for the compression and expansion processes. We confirm the fluctuation theorem from the ratio of the two distributions. We also show that the average values of work for the two processes comply with the Jarzynski equality. This system has an analogy with a gas in a breathing soft wall. We discuss about its applicability to a heat engine and an information engine operated by feedback control.
Collapse
Affiliation(s)
- Dong Yun Lee
- Department of Physics, Pusan National University, Pusan 609-735, Korea and Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 689-798, Korea
| | - Chulan Kwon
- Department of Physics, Myongji University, Gyeonggi-Do 449-728, Korea
| | - Hyuk Kyu Pak
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 689-798, Korea and Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 689-798, Korea
| |
Collapse
|
7
|
Nostheide S, Holubec V, Chvosta P, Maass P. Unfolding kinetics of periodic DNA hairpins. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:205102. [PMID: 24785383 DOI: 10.1088/0953-8984/26/20/205102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
DNA hairpin molecules with periodic base sequences can be expected to exhibit a regular coarse-grained free energy landscape (FEL) as a function of the number of open base pairs and applied mechanical force. Using a commonly employed model, we first analyze for which types of sequences a particularly simple landscape structure is predicted, where forward and backward energy barriers between partly unfolded states are decreasing linearly with force. Stochastic unfolding trajectories for such molecules with simple FEL are subsequently generated by kinetic Monte Carlo simulations. Introducing probabilities that can be sampled from these trajectories, it is shown how the parameters characterizing the FEL can be estimated. Already 300 trajectories, as typically generated in experiments, provide faithful results for the FEL parameters.
Collapse
Affiliation(s)
- Sandra Nostheide
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
| | | | | | | |
Collapse
|
8
|
Kwon C, Noh JD, Park H. Work fluctuations in a time-dependent harmonic potential: rigorous results beyond the overdamped limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062102. [PMID: 24483381 DOI: 10.1103/physreve.88.062102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2013] [Indexed: 06/03/2023]
Abstract
We investigate the stochastic motion of a Brownian particle in the harmonic potential with a time-dependent force constant. It may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time-dependent field. We use the path integral formalism to solve the Langevin equation and the associated Fokker-Planck (Kramers) equation. Rigorous relations are derived to generate the probability density function for the time-dependent nonequilibrium work production beyond the overdamped limit. We find that the work distribution exhibits an exponential tail with a power-law prefactor, accompanied by an interesting oscillatory feature (multiple pseudo-locking-unlocking transitions) due to the inertial effect. Some exactly solvable cases are discussed in the overdamped limit.
Collapse
Affiliation(s)
- Chulan Kwon
- Department of Physics, Myongji University, Yongin, Gyeonggi-Do 449-728, Korea
| | - Jae Dong Noh
- Department of Physics, University of Seoul, Seoul 130-743, Republic of Korea and School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
| | - Hyunggyu Park
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
| |
Collapse
|
9
|
Seifert U. Stochastic thermodynamics, fluctuation theorems and molecular machines. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:126001. [PMID: 23168354 DOI: 10.1088/0034-4885/75/12/126001] [Citation(s) in RCA: 1171] [Impact Index Per Article: 97.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Collapse
Affiliation(s)
- Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| |
Collapse
|
10
|
Kwon C, Ao P. Nonequilibrium steady state of a stochastic system driven by a nonlinear drift force. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061106. [PMID: 22304039 DOI: 10.1103/physreve.84.061106] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2011] [Revised: 09/24/2011] [Indexed: 05/31/2023]
Abstract
We investigate the properties of the nonequilibrium steady state for the stochastic system driven by a nonlinear drift force and influenced by noises that are not identically and independently distributed. The nonequilibrium steady state (NESS) current results from a residual part of the drift force that is not canceled by the diffusive action of noises. From our previous study for the linear drift force, the NESS current was found to circulate on the equiprobability surface with the maximum at a stable fixed point of the drift force. For the nonlinear drift force, we use the perturbation theory with respect to the cubic and quartic coefficients of the drift force. We find an interesting potential landscape picture where the probability maximum shifts from the fixed point of the drift force and, furthermore, the NESS current has a nontrivial circulation that flows off the equiprobability surface and has various centers not located at the probability maximum. The theoretical result is well confirmed by the computer simulation.
Collapse
Affiliation(s)
- Chulan Kwon
- Department of Physics, Myongji University, Yongin, Gyeonggi-Do 449-728, Republic of Korea.
| | | |
Collapse
|
11
|
Hahn AM, Then H. Measuring the convergence of Monte Carlo free-energy calculations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041117. [PMID: 20481687 DOI: 10.1103/physreve.81.041117] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2009] [Revised: 02/24/2010] [Indexed: 05/29/2023]
Abstract
The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free-energy based on work measurements of nonequilibrium, finite-time processes, and their reversed counterparts by applying Bennett's acceptance ratio method. A nice property of this method is that each free-energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free-energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett's acceptance ratio method.
Collapse
Affiliation(s)
- Aljoscha M Hahn
- Institut für Physik, Carl von Ossietzky Universität, 26111 Oldenburg, Germany
| | | |
Collapse
|
12
|
Hahn AM, Then H. Characteristic of Bennett's acceptance ratio method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031111. [PMID: 19905066 DOI: 10.1103/physreve.80.031111] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2009] [Indexed: 05/28/2023]
Abstract
A powerful and well-established tool for free-energy estimation is Bennett's acceptance ratio method. Central properties of this estimator, which employs samples of work values of a forward and its time-reversed process, are known: for given sets of measured work values, it results in the best estimate of the free-energy difference in the large sample limit. Here we state and prove a further characteristic of the acceptance ratio method: the convexity of its mean-square error. As a two-sided estimator, it depends on the ratio of the numbers of forward and reverse work values used. Convexity of its mean-square error immediately implies that there exists a unique optimal ratio for which the error becomes minimal. Further, it yields insight into the relation of the acceptance ratio method and estimators based on the Jarzynski equation. As an application, we study the performance of a dynamic strategy of sampling forward and reverse work values.
Collapse
Affiliation(s)
- Aljoscha M Hahn
- Institut für Physik, Carl von Ossietzky Universität, 26111 Oldenburg, Germany
| | | |
Collapse
|