Fluctuation Relation beyond Linear Response Theory
arXiv:cond-mat/0412455 · doi:10.1007/s10955-005-3021-5
Abstract
The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals T as T goes to infinity and it is a generalization of the fluctuation--dissipation theorem to far from equilibrium systems in a steady state which reduces to the usual Green-Kubo (GK) relation in the limit of small external non conservative forces. FR is a theorem for smooth uniformly hyperbolic systems, and it is assumed to be true in all dissipative ``chaotic enough'' systems in a steady state. In this paper we develop a theory of finite time corrections to FR, needed to compare the asymptotic prediction of FR with numerical observations, which necessarily involve fluctuations of observables averaged over finite time intervals T. We perform a numerical test of FR in two cases in which non Gaussian fluctuations are observable while GK does not apply and we get a non trivial verification of FR that is independent of and different from linear response theory. Our results are compatible with the theory of finite time corrections to FR, while FR would be observably violated, well within the precision of our experiments, if such corrections were neglected.
Version accepted for publication on the Journal of Statistical Physics; minor changes; two references added
References in corpus (12)
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Dynamical ensembles in stationary states
- Scaling behavior in the -relaxation regime of a supercooled Lennard-Jones mixture
- Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
- Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
- A fluidized granular medium as an instance of the Fluctuation Theorem
- Chaotic principle: an experimental test
- SRB states and nonequilibrium statistical mechanics close to equilibrium
- Entropy production in nonequilibrium thermodynamics: a review
- Reversibility, coarse graining and the chaoticity principle
- Time-reversible Dynamical Systems for Turbulence
- Fluctuations of entropy production in the isokinetic ensemble
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