This volume provides a systematic mathematical exposition of the
conceptual problems of nonequilibrium statistical physics, such as
entropy production, irreversibility, and ordered phenomena. Markov
chains, diffusion processes, and hyperbolic dynamical systems are
used as mathematical models of physical systems. A
measure-theoretic definition of entropy production rate and its
formulae in various cases are given. It vanishes if and only if the
stationary system is reversible and in equilibrium. Moreover, in
the cases of Markov chains and diffusion processes on manifolds, it
can be expressed in terms of circulations on directed cycles.
Regarding entropy production fluctuations, the Gallavotti-Cohen
fluctuation theorem is rigorously proved.
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