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Time-reversal symmetry relations for fluctuating currents in nonequilibrium systems. (English) Zbl 1371.82087

Summary: Fluctuation relations for currents are established in several classes of systems. For the effusion of noninteracting particles through a small hole in a thin wall, a fluctuation relation for the particle current is directly proved from the Hamiltonian microdynamics by constructing the exact invariant probability measure, which is shown to break time-reversal symmetry under nonequilibrium conditions. Current fluctuation relations are also obtained for the stochastic processes ruled by the Smoluchowski and Fokker-Planck master equations by modifying the master operator with the current counting parameters. Finally, the same method is applied to the coarse-grained master equation of the fluctuating Boltzmann equation to establish the fluctuation relation for the currents in dilute or rarefied gases.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
58J70 Invariance and symmetry properties for PDEs on manifolds
81S22 Open systems, reduced dynamics, master equations, decoherence
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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