Luc Rey-Bellet (University of Massachusetts)
Title: Thermodynamics of non-equilibrium steady states, entropy production and fluctuations.
a non-equilibrium steady state is obtained by driving and maintaining a
system out of equilibrium by a combination of thermostats and external
non-Hamiltonian driving forces. Mathematically the
non-equilibrium steady state is characterized by time-reversal symmetry
breaking, i.e., lack of detailed balance. Entropy production
is a direct observable which measures this symmetry breaking and whose
fluctuations turn out to exhibit remarkable universal properties: the
Gallavotti-Cohen fluctuation theorem which is a far from equilibrium
generalization of Kubo formula and Onsager relations.
will discussed in great generality both for deterministic and
stochastic dynamics. Contrary to equilibrium statistical
mechanics where the Gibbs ansatz provide a a detailed description of
the steady state, for nonequilibrium steady states a detailed
knowledge of the dynamics and its ergodic properties is necessary
to understand the steady state. These properties are
naturally formulated in terms of ergodic and probabilistic
properties for the dynamics of the systems: ergodicity and
mixing, central limit theorem and large deviations.
part of our lecture will consist of the exposition of a general
framework to understand the structure of steady states. The
second part of the lectures will deals with a number of examples which
have been analyzed rigorously : a) Nonequilibrium molecular
dynamics. b) Thermostated Hamiltonian systems. c) Jump
processes. Finally in the third part of the lecture we
introduces and analyze a large new class of nonequilibrium models based
on game theoretic considerations.