**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
tel +39-06-4991-4370
fax +39-06-4957697
**

**em: giovanni.gallavotti@roma1.infn.it
http://ipparco.roma1.infn.it
**