Erratum: “Fluctuation theorem and Onsager reciprocity relations” [J. Chem. Phys. 121, 6167 (2004)]

Andrieux, David; Gaspard, Pierre

doi:10.1063/1.2400030

Cited by 71 publications

(177 citation statements)

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“…The past decade has brought new insights into nonequilibrium statistical mechanics due to the discovery of various types of fluctuation relations valid arbitrarily far from equilibrium [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. These relations identify, at the level of the single realization of a statistical ensemble, the "trajectory entropy" which upon ensemble averaging reproduce the thermodynamic entropy.…”

Section: Introductionmentioning

confidence: 99%

“…Previously derived FTs are recovered by considering specific types of nonequilibrium transformations. Steady state FTs [6,12,13] are obtained for systems maintained in a nonequilibrium steady state (NESS) between reservoirs with different thermodynamic properties. The Jarzynski or Crooks type FTs [4,8,9] are derived for systems initially at equilibrium with a single reservoir which are externally driven out of equilibrium by an external force.…”

Section: Introductionmentioning

confidence: 99%

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Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

2007

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The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: an arbitrary nonequilibrium transformation always produces a change in the total entropy production greater or equal than the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

2007

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“…Another consequence of microreversibility are the so-called fluctuation theorems, which characterize the large fluctuations of physical quantities in nonequilibrium systems. They have been derived in deterministic [3,4,5,6] or Markovian stochastic systems [7,8,9,10] and concern different quantities such as the entropy production [5], the dissipated work [11,12], or the currents crossing the system in a nonequilibrium situation [13,14,15]. Such relations are important because they are valid far from equilibrium.…”

Section: Introductionmentioning

confidence: 99%

“…Such relations are important because they are valid far from equilibrium. Close enough to equilibrium where the response of the system is linear in the affinities, the Onsager reciprocity relations can be deduced from the fluctuation theorem [6,8,13].…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, we use a fluctuation theorem for the currents which was first proven for mechanically driven Markovian processes [8,9,10], then in the more general framework of Schnakenberg network theory [16] which includes reactive processes [13,14], as well as in non-Markovian situations [17]. This fluctuation theorem directly concerns the generating function of the different fluctuating currents crossing a nonequilibrium system.…”

Section: Introductionmentioning

confidence: 99%

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A fluctuation theorem for currents and non-linear response coefficients

2007

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We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond Onsager reciprocity relations.

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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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Erratum: “Fluctuation theorem and Onsager reciprocity relations” [J. Chem. Phys. 121, 6167 (2004)]

Cited by 71 publications

References 0 publications

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

A fluctuation theorem for currents and non-linear response coefficients

Time Asymmetry in Nonequilibrium Statistical Mechanics

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