Entropy production in driven spatially extended systems

This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production can be identified with a logarithmic ratio of microstate multiplicities of the original macrostate with respect to the time-reversed state. A special role is taken by Gibbs measures for the stationary spatio-temporal distribution of trajectories. The mean entropy production is always nonnegative and it is zero only when the system is in equilibrium. The fluctuations of the entropy production satisfy a symmetry first observed in Evans et al. (1993) and then derived in Gallavotti and Cohen (1995a,b) for the phase-space contraction rate in a class of strongly chaotic dynamical systems. Aspects of the general framework are illustrated via a bulk driven diffusive lattice gas.