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Condensed Matter > Statistical Mechanics

arXiv:cond-mat/0612397 (cond-mat)
[Submitted on 15 Dec 2006]

Title:Gallavotti-Cohen theorem, Chaotic Hypothesis and the zero-noise limit

Authors:Jorge Kurchan
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Abstract: The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat - the Gallavotti-Cohen Theorem -- relies on the ergodic properties of the system considered. We show that when perturbed by an energy-conserving random noise, the relation follows trivially for any system at finite noise amplitude. The time needed to achieve stationarity may stay finite as the noise tends to zero, or it may diverge. In the former case the Gallavotti-Cohen result is recovered, while in the latter case, the crossover time may be computed from the action of `instanton' orbits that bridge attractors and repellors. We suggest that the `Chaotic Hypothesis' of Gallavotti can thus be reformulated as a matter of stochastic stability of the measure in trajectory space. In this form this hypothesis may be directly tested.
Subjects: Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)
Cite as: arXiv:cond-mat/0612397 [cond-mat.stat-mech]
  (or arXiv:cond-mat/0612397v1 [cond-mat.stat-mech] for this version)
  https://doi.org/10.48550/arXiv.cond-mat/0612397
Related DOI: https://doi.org/10.1007/s10955-007-9368-z

Submission history

From: Jorge Kurchan [view email]
[v1] Fri, 15 Dec 2006 14:18:33 UTC (40 KB)
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