Dissipative Transport

Nonequilibrium stationary states (NESS) describe the state of a mechanical system driven and maintained out of equilibrium by external forces. The main characteristic of a NESS is that it sustains sustain steady flows or equivalently that it exhibits positive entropy production. We discuss general features of the fluctuations of the entropy production and corresponding flows. The NESS and the entropy production have been formally defined in the entry ”Nonequilibrium Stationary States” to which we refer for details. A probability measure for ν is a NESS for the dynamical system (M,Φt) with a given reference measure μ if ν is ergodic and is an SRB-measure with respect to μ. The corresponding entropy production σ is defined by σ(x) = d dt log dμt dμ |t=0. In comparison to the theory of equilibrium states in statistical mechanics little is known about the general properties of NESS. A notable exception is a general and striking universal property of the fluctuations of the entropy production in the NESS which occur if the system is time-reversible, i.e. if there exists an involution i of the phase space M such that, for all t,