Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats

Abstract

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics which satisfy natural properties under time reversal. Next, we discuss the characterization of the stationary state as the solution of a variational principle and its relation to the minimum entropy production principle. Finally, we compute the large deviation functional of the current in the case of a harmonic chain thermostated by a Gaussian stochastic coupling.

Revised version, published in Journal of Statistical Physics

References in corpus (6)

• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Steady state statistics of driven diffusions
• Cumulants and large deviations of the current through non-equilibrium steady states
• Minimum entropy production principle from a dynamical fluctuation law
• On and beyond entropy production: the case of Markov jump processes
• Gallavotti-Cohen theorem, Chaotic Hypothesis and the zero-noise limit

Cited by in corpus (3)

• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Fluctuations and response of nonequilibrium states
• Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs