Existence of Transport Coefficients

We discuss the rigorous results on the existence of transport coefficients in the (deterministic) dynamical systems. This fundamental problem of the nonequilibrium statistical mechanics has been so far solved only for some models of the Lorentz gas and for some systems of hard spheres. The natural hierarchy of models based on a number of moving particles in the system allows to determine the simplest models where the corresponding transport coefficients may exist. It also suggests a strategy for the future studies in this area.

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