Abstract
We propose, as a generalization of an idea of Ruelle's 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 nonequilibrium states and it leads to the identification of a unique distribution μ 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 μ: 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 nontrivial, 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.
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Gallavotti, G., Cohen, E.G.D. Dynamical ensembles in stationary states. J Stat Phys 80, 931–970 (1995). https://doi.org/10.1007/BF02179860
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DOI: https://doi.org/10.1007/BF02179860