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FluctuationDissipation: Response Theory in Statistical Physics
 PHYSICS REPORTS 461 (2008) 111195
, 2008
"... ..."
TimeReversal and Entropy
, 2002
"... There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of timereversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phasespace contraction and timer ..."
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Cited by 16 (7 self)
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There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of timereversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phasespace contraction and timereversal starting from a deterministic dynamics. Both closed and open systems, in the transient and in the steady regime, are considered. The main result identifies under general conditions the statistical mechanical entropy production as the source term of timereversal breaking in the path space measure for the evolution of reduced variables. This provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful (in)equalities. We also discuss the Markov approximation. Important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior.
Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
 SUBMITTED TO: NONLINEARITY
, 2007
"... The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical “fluctuation relations” describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, ..."
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Cited by 10 (0 self)
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The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical “fluctuation relations” describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, in stochastic frameworks. Other results first obtained for stochastic processes, and later considered in deterministic dynamics, describe the temporal evolution of fluctuations. The field has grown beyond expectation: research works and different perspectives are proposed at an ever faster pace. Indeed, understanding fluctuations is important for the emerging theory of nonequilibrium phenomena, as well as for applications, such as those of nanotechnological and biophysical interest. However, the links among the different approaches and the limitations of these approaches are not fully understood. We focus on these issues, providing: a) analysis of the theoretical models; b) discussion of the rigorous mathematical results; c) identification of the physical mechanisms
Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
, 2010
"... Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or EvansSearles) and Steady State (or GallavottiCohen) Fluctuation Theorems of nonequilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathemati ..."
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Cited by 5 (3 self)
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Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or EvansSearles) and Steady State (or GallavottiCohen) Fluctuation Theorems of nonequilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. Besides its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.
Entropic fluctuations of quantum dynamical semigroups
"... We study a class of finite dimensional quantum dynamical semigroups {e tL}t≥0 whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroups arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of eq ..."
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Cited by 4 (2 self)
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We study a class of finite dimensional quantum dynamical semigroups {e tL}t≥0 whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroups arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. We prove a general entropic fluctuation theorem for this class of semigroups by relating the cumulant generating function of entropy transport to the spectrum of a family of deformations of the generator L. We show that, besides the celebrated EvansSearles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux et al., and that in the linear regime near equilibrium these two symmetries yield Kubo’s and Onsager’s linear response relations.
ELEMENTS OF NONEQUILIBRIUM STATISTICAL MECHANICS
"... 1.2. The plan 6 2. Elements of an Htheorem 7 ..."
ReyBellet: Entropic Fluctuations in
 Statistical Mechanics I. Classical Dynamical Systems, Nonlinearity
, 2011
"... ..."
TIMEREVERSAL AND ENTROPY
, 2002
"... There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of timereversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phasespace contraction and time ..."
Abstract
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There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of timereversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phasespace contraction and timereversal starting from a deterministic dynamics. Both closed and open systems, in the transient and in the steady regime, are considered. The main result identifies under general conditions the statistical mechanical entropy production as the source term of timereversal breaking in the path space measure for the evolution of reduced variables. This provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful (in)equalities. We also discuss the Markov approximation. Important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior.
STATISTICAL MECHANICS OF ENTROPY PRODUCTION: Gibbsian Hypothesis and . . .
, 2008
"... It is argued that a Gibbsian formula for the spacetime distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy production is naturally expressed as the timereversal symm ..."
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It is argued that a Gibbsian formula for the spacetime distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy production is naturally expressed as the timereversal symmetry breaking part of the spacetime action functional. Its mean is always positive. This is both supported by a Boltzmann type analysis by counting the change in phase space extension corresponding to the macrostate as by various examples of nonequilibrium models. As the Gibbsian setup allows for nonMarkovian dynamics, we also get a local fluctuation theorem for the entropy production in globally Markovian models. In order to study the response of the system to perturbations, we can apply the standard Gibbs formalism.
Large deviations and Gallavotti–Cohen principle for dissipative PDE’s with rough noise
, 2014
"... We study a class of dissipative PDE’s perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to the space variables and has a nondegenerate law, we prove t ..."
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We study a class of dissipative PDE’s perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to the space variables and has a nondegenerate law, we prove that the system in question satisfies a large deviation principle (LDP) in τtopology. Under some additional hypotheses, we establish a Gallavotti–Cohen type symmetry for the rate function of an entropy production functional and the strict positivity and finiteness of the mean entropy production in the stationary regime. The latter result is applicable to PDE’s with strong nonlinear dissipation.