Random paths and current fluctuations in nonequilibrium statistical mechanics (Q2879380)

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.