Energy fluctuations in simple conduction models

TL;DR

This paper introduces stochastic lattice models for heat conduction in solids, analyzing energy fluctuations at equilibrium and deriving hydrodynamic limits of the fluctuation field in certain cases.

Contribution

It presents a new class of stochastic weakly coupled map lattices as models for heat conduction, with analysis of energy fluctuations and hydrodynamic limits.

Findings

Energy fluctuations at equilibrium analyzed.

Hydrodynamic limits derived in some cases.

Models capture key features of heat conduction in solids.

Abstract

We introduce a class of stochastic weakly coupled map lattices, as models for studying heat conduction in solids. Each particle on the lattice evolves according to an internal dynamics that depends on its energy, and exchanges energy with its neighboors at a rate that depends on its internal state. We study energy fluctuations at equilibrium in a diffusive scaling. In some cases, we derive the hydordynamic limit of the fluctuation field.