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FM 2004-10; mp_arc 04-159, math.DS/0405420 Journal of Statistical Physics, 119, 909--944, 2005

Author: Alessandro Giuliani, Francesco Zamponi, Giovanni Gallavotti

Title: Fluctuation Relation beyond Linear Response Theory

The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals $\t$ as $\t\to\io$ 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 {\it independent of} and {\it different from} linear response theory. Our results are compatible with the theory of finite time corrections to FR, while FR would be {\it observably violated}, well within the precision of our experiments, if such corrections were neglected.

Giovanni Gallavotti
Fisica, Universita' di Roma 1
P.le Moro 2
00185 Roma, Italia
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em: giovanni.gallavotti@roma1.infn.it
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