 9532 G. Gallavotti, E.G.D. Cohen
 Dynamical ensembles in stationary states
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Jan 28, 95

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Abstract. 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, parameterfree, 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 KolmogorovObuchov theory for
turbulent flow.
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