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Random paths and current fluctuations in nonequilibrium statistical mechanics. (English) Zbl 1298.82051

This paper is an overview of those results which have been obtained in non-equilibrium statistical mechanics in the framework of Hamiltonian classical or quantum dynamics combined with the theory of stochastic processes. One reviews successively chaos-transport modelling, statistics of random paths, statistics of current fluctuations, equilibrium systems. In the considered approach the statistics of random events is performed in time or space-time exactly like the equilibrium statistical mechanics where statistics is performed in space. Various large-deviation relationships can be established between non-equilibrium properties such as transport coefficients, entropy production and other parameters which characterize the underlying microscopic Hamiltonian dynamics.

MSC:

82C35 Irreversible thermodynamics, including Onsager-Machlup theory
82C70 Transport processes in time-dependent statistical mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
81S22 Open systems, reduced dynamics, master equations, decoherence
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