DYNAMICAL ENSEMBLES IN STATIONARY STATES

We propose, as a generalization of an idea of Ruelle's to describe tur bulent fluid flow, a chaotic hypothesis for reversible dissipative man y-particle systems in nonequilibrium stationary states in general. Thi s implies an extension of the zeroth law of thermodynamics to nonequil ibrium states and it leads to the identification of a unique distribut ion mu describing the asymptotic properties of the time evolution of t he system for initial data randomly chosen with respect to a uniform d istribution on phase space. For conservative systems in thermal equili brium the chaotic hypothesis implies the ergodic hypothesis. We outlin e a procedure to obtain the distribution mu: it leads to a new unifyin g point of view for the phase space behavior of dissipative and conser vative systems. The chaotic hypothesis is confirmed in a nontrivial, p arameter-free, way by a recent computer experiment on the entropy prod uction fluctuations in a shearing fluid Far from equilibrium. Similar applications to other models are proposed, in particular to a model fo r the Kolmogorov-Obuchov theory for turbulent flow.