Some recent developments in
non-equilibrium statistical physics
K MALLICK
Institut de Physique Th\'eorique, CEA Saclay, 91191
E-mail: kirone.mallick@cea.fr
Abstract. We first recall
the laws of classical
thermodynamics
and the fundamental principles of
statistical
mechanics
and emphasize the fact that the fluctuations of a system
in
macroscopic equilibrium, such as Brownian motion, can be
explained by
statistical
mechanics and not by thermodynamics. In
the vicinity of
equilibrium, the susceptibility of a system to an
infinitesimal
external
perturbation is related to the amplitude of the
fluctuations
at equilibrium (Einstein's relation)
and exhibits a
symmetry
discovered by Onsager. We shall then focus on the
mathematical
description of systems out of
equilibrium using
Markovian dynamics. This
will allow us to present some remarkable
relations derived during the last decade and valid arbitrarily
far from equilibrium: the Gallavotti--Cohen fluctuation theorem and
Jarzynski's
non-equilibrium work identities. These recent results
will
be illustrated by applying them to
simple systems such as the
Brownian ratchet
model for molecular motors and the asymmetric
exclusion
process which is a basic example of a
driven lattice gas.
Keywords. Thermodynamics; non-equilibrium
mechanics; Brownian
motion; molecular motors; Gallavotti--Cohen fluctuation theorem;
Jarzynski's work relation.
PACS Nos 05.70.Ln; 05.40.-a; 87.16.Nn