Hot scatterers and tracers for the transfer of heat in collisional dynamics

TL;DR

This paper develops stochastic models for heat transfer in collisional systems with tracer particles and hot scatterers, analyzing their ergodic properties and energy current fluctuations, revealing different temperature profiles depending on particle mobility.

Contribution

It introduces Markov renewal process models for heat transport in collisional dynamics and analyzes their ergodic properties and energy current fluctuations.

Findings

The cumulant generating function is non-analytic out of equilibrium.

Linear temperature profile when particles move freely.

Nonlinear temperature profile when particles are confined.

Abstract

We introduce stochastic models for the transport of heat in systems described by local collisional dynamics. The dynamics consists of tracer particles moving through an array of hot scatterers describing the effect of heat baths at fixed temperatures. Those models have the structure of Markov renewal processes. We study their ergodic properties in details and provide a useful formula for the cumulant generating function of the time integrated energy current. We observe that out of thermal equilibrium, the generating function is not analytic. When the set of temperatures of the scatterers is fixed by the condition that in average no energy is exchanged between the scatterers and the system, different behaviours may arise. When the tracer particles are allowed to travel freely through the whole array of scatterers, the temperature profile is linear. If the particles are locked in between scatterers, the temperature profile becomes nonlinear. In both cases, the thermal conductivity is interpreted as a frequency of collision between tracers and scatterers.