Fluctuation theorem for stochastic dynamics

Kurchan, Jorge

doi:10.1088/0305-4470/31/16/003

Cited by 1,058 publications

(1,462 citation statements)

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“…Open, driven chemical and molecular systems far from chemical equilibrium have been studied from several different points of view in statistical physics. In terms of stochastic processes, these investigations include "nonequilibrium potentials" [1,4,5], "dissipative structures" [36], "cycle kinetics" [16,37,38], "Brownian motors" [39,16], "stochastic resonance" [40], and "fluctuation theorems" [11,12,15,18]. The result we obtain in this work, in terms of a Jarzynski-type equality, clearly demonstrates an intimate connection between the fluctuation theorems and the nonequilibrium potentials.…”

Section: Discussionsupporting

confidence: 62%

“…FTs were first developed in the context of microcanonical chaotic dynamical systems [9,10]. It has also been studied in parallel for stochastic canonical dynamics [11,12]. In this paper, we first present our results via a simple example: a 3-state, driven cyclic reaction widely found in biochemistry.…”

Section: Introductionmentioning

confidence: 99%

“…(Though seldomly it has been presented in this way.) To introduce the new results from the recent work on FTs [11,12,15], we first define the irreversible heat dissipation following a stochastic trajectory in a NESS, Q irr (t).…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Qian

2005

J. Phys. Chem. B

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Applying the method from recently developed fluctuation theorems to the stochastic dynamics of single macromolecules in ambient fluid at constant temperature, we establish two Jarzynski-type equalities: (1) between the log-mean-exponential (LME) of the irreversible heat dissiption of a driven molecule in nonequilibrium steady-state (NESS) and ln P ness (x), and (2) between the LME of the work done by the internal force of the molecule and nonequilibrium chemical potential function µ ness (x) ≡ U(x) + k B T ln P ness (x), where P ness (x) is the NESS probability density in the phase space of the macromolecule and U(x) is its internal potential function. Ψ = µ ness (x)P ness (x)dx is shown to be a nonequilibrium generalization of the Helmholtz free energy and ∆Ψ = ∆U−T ∆S for nonequilibrium processes, where S = −k B P (x) ln P (x)dx is the Gibbs entropy associated with P (x). LME of heat dissipation generalizes the concept of entropy, and the equalities define thermodynamic potential functions for open systems far from equilibrium.

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Section: Discussionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Qian

2005

J. Phys. Chem. B

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“…[4], it was formulated as an extension of Onsager's reciprocity relation. Furthermore, the fluctuation theorem is not restricted to dynamical systems, and was also confirmed for the Langevin system [5], for general stochastic systems [6], and for the master equation [10,13]. In ref.…”

Section: Introductionmentioning

confidence: 92%

“…To elucidate the nature of these fluctuations is an issue of nonequilibrium statistical physics in last two decades, for instance, in refs. [1,2,3,4,5,6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

The McLennan–Zubarev steady state distribution and fluctuation theorems

Sano

2017

Physica A: Statistical Mechanics and its Applications

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The McLennan-Zubarev steady state distribution is studied in the connection with fluctuation theorems. We derive the McLennan-Zubarev steady state distribution from the nonequilibrium detailed balance relation. Then, considering the cumulant function or cumulant functional, two fluctuation theorems for entropy and for currents are proved. Using the fluctuation theorem for currents, the current is expanded in terms of thermodynamic forces. In the lowest order of the thermodynamic force, we find that the transport coefficient satisfies the Onsager's reciprocal relation. In the next order, we derived the correction term to the Green-Kubo formula.

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Time Asymmetry in Nonequilibrium Statistical Mechanics

Gaspard

2007

Advances in Chemical Physics

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An overview is given on the recent understanding of time asymmetry in nonequilibrium statistical mechanics. This time asymmetry finds its origin in the spontaneous breaking of the time-reversal symmetry at the statistical level of description. The relaxation toward the equilibrium state can be described in terms of eigenmodes of fundamental Liouville's equation of statistical mechanics. These eigenmodes are associated with Pollicott-Ruelle resonances and correspond to exponential damping. These eigenmodes can be explicitly constructed in dynamical systems sustaining deterministic diffusion, which shows their singular character. The entropy production expected from nonequilibrium thermodynamics can be derived ab initio thanks to this construction. In the escape-rate theory, the transport coefficients can be related to the leading Pollicott-Ruelle resonance of open systems and to the characteristic quantities of the microscopic dynamics. In nonequilibrium steady states, the entropy production is shown to result from a time asymmetry in the dynamical randomness of the nonequilibrium fluctuations. Furthermore, the generalizations of Onsager reciprocity relations to nonlinear response can be deduced from the fluctuation theorem for the currents. Furthermore, the principle of temporal ordering in nonequilibrium steady states is formulated and its perspectives for the generation of biological information are discussed.

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Fluctuation theorem for stochastic dynamics

Cited by 1,058 publications

References 10 publications

Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

The McLennan–Zubarev steady state distribution and fluctuation theorems

Time Asymmetry in Nonequilibrium Statistical Mechanics

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