Thermal contact through a two-temperature kinetic Ising chain

Abstract

We consider a model for thermal contact through a diathermal interface between two macroscopic bodies at different temperatures: an Ising spin chain with nearest neighbor interactions is endowed with a Glauber dynamics with different temperatures and kinetic parameters on alternating sites. The inhomogeneity of the kinetic parameter is a novelty with respect to the model of Ref.[1] and we exhibit its influence upon the stationary non equilibrium values of the two-spin correlations at any distance. By mapping to the dynamics of spin domain walls and using free fermion techniques, we determine the scaled generating function for the cumulants of the exchanged heat amounts per unit of time in the long time limit.1 In Ref.[5] the terminology "generalized" detailed balance is used. 2 We notice that the first requirement is not satisfied by the Ising chain model of Ref.[7], where two thermostats at different temperatures act on every spin : the latter model does not describe a situation of thermal contact.