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

Gaspard, Pierre

J. Math. Phys. 55, No. 7, 075208, 20 p. (2014).

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.

Reviewer: Guy Jumarie (Montréal)

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

Keywords:

non-equilibrium statistical mechanics; chaos; transport; random paths; entropy; quantum systems

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