Heat flow in chains driven by thermal noise

Abstract

We consider the large deviation function for a classical harmonic chain composed of N particles driven at the end points by heat reservoirs, first derived in the quantum regime by Saito and Dhar (2007Phys.Rev.Lett.99180601) and in the classical regime by Saito and Dhar (2011Phys.Rev.E83041121) and Kundu et al (2011J.Stat.Mech.P03007). Within a Langevin description we perform this calculation on the basis of a standard path integral calculation in Fourier space. The cumulant generating function yielding the large deviation function is given in terms of a transmission Green's function and is consistent with the fluctuation theorem. We find a simple expression for the tails of the heat distribution, which turns out to decay exponentially. We, moreover, consider an extension of a single-particle model suggested by Derrida and Brunet (2005 Einstein Aujourd'hui (Les Ulis: EDP Sciences)) and discuss the two-particle case. We also discuss the limit for large N and present a closed expression for the cumulant generating function. Finally, we present a derivation of the fluctuation theorem on the basis of a Fokker-Planck description. This result is not restricted to the harmonic case but is valid for a general interaction potential between the particles. © 2012 IOP Publishing Ltd.