5 - Fluctuation Relations for Energy and Particle Fluxes

Summary

The fluctuations of energy and particle fluxes obey remarkable symmetries called fluctuation relations, which are valid arbitrarily far from equilibrium and find their origin in microreversibility. Yet they imply the nonnegativity of entropy production in accord with the second law of thermodynamics. They express the directionality of nonequilibrium processes, reducing at equilibrium to the conditions of detailed balance. The nonequilibrium work fluctuation relation and Jarzynski’s equality are presented in the absence and the presence of a magnetizing field and also for joint angular momentum transfer. Moreover, the multivariate fluctuation relation for all the fluxes across an open system in contact with several reservoirs is deduced from both the classical Hamiltonian microdynamics and the theory of stochastic processes. The multivariate fluctuation relation implies not only the fluctuation–dissipation theorem and the Onsager–Casimir reciprocal relations close to equilibrium but also their generalizations to the nonlinear response properties of relevance farther away from equilibrium.