We propose as a generalization of an idea of Ruelle to describe turbulent
fluid flow a chaotic hypothesis for reversible dissipative many particle
systems in nonequilibrium stationary states in general. This implies an
extension of the zeroth law of thermodynamics to non equilibrium states and it
leads to the identification of a unique distribution \m describing the
asymptotic properties of the time evolution of the system for initial data
randomly chosen with respect to a uniform distribution on phase space. For
conservative systems in thermal equilibrium the chaotic hypothesis implies the
ergodic hypothesis. We outline a procedure to obtain the distribution \m: it
leads to a new unifying point of view for the phase space behavior of
dissipative and conservative systems. The chaotic hypothesis is confirmed in a
non trivial, parameter--free, way by a recent computer experiment on the
entropy production fluctuations in a shearing fluid far from equilibrium.
Similar applications to other models are proposed, in particular to a model for
the Kolmogorov--Obuchov theory for turbulent flow.Comment: 31 pages, 3 figures, compile with dvips (otherwise no pictures