Temperature Profiles in Hamiltonian Heat Conduction

TL;DR

This paper derives a universal law for temperature profiles in Hamiltonian heat conduction models, revealing how energy-exchange mechanisms influence the profile shape through a parameter.

Contribution

It introduces a universal law for temperature profiles in Hamiltonian and stochastic models, linking the profile shape to energy-exchange mechanisms via a parameter.

Findings

The temperature profile follows a universal law with a parameter .

Linear profiles occur only when =1.

Energy-exchange mechanisms determine the value of .

Abstract

We study heat transport in the context of Hamiltonian and related stochastic models with nearest-neighbor coupling, and derive a universal law for the temperature profiles of a large class of such models. This law contains a parameter $\alpha$, and is linear only when $\alpha=1$. The value of $\alpha$ depends on energy-exchange mechanisms, including the range of motion of tracer particles and their times of flight.