Nonequilibrium Statistical Mechanics: Stochastic thermodynamics and heat conduction in low dimensional systeMS

Abstract

I review the main results of stochastic thermodynamics, for systems under external driving or in a nonequilibrium steady state. These include Crook’s identity, Jarzynski relation and Gallovati-Cohen fluctuation theorem rem. These give the ratio of probability of entropy production for a trajectory of the system to that of the time-reversed trajectory, and therefore can be thought of as a natural generalization of the second law of thermodynamics. After outlining the derivations of these results, various sources of entropy productions are illustrated for the exclusion process. Though the theorems are valid under very general conditions, their applicability is restricted as the quantities appearing are not always directly measurable. However, one recovers near-equilibrium results as limiting cases. The second part of the thesis is a review of calculations of thermal con- conductivity for some low dimensional models. The first is a chain of identity- cal harmonic oscillators, with nearest-neighbor interactions, coupled at its ends to stochastic reservoirs at different temperatures. The system is found to have infinite thermal conductivity in the thermodynamic limit. A more realistic model, the harmonic chain with mass disorder is considered next, and the dependence of thermal conductivity on system size L is found to be √ L. Lastly the disordered Lorentz gas is is shown to have finite thermal conductivity.