On the Conversion of Work into Heat: Microscopic Models and Macroscopic Equations

TL;DR

This paper investigates the microscopic and macroscopic behavior of a harmonic chain system with heat baths and external forces, deriving a heat equation with a discontinuous slope and exploring extensions to higher dimensions and more complex interactions.

Contribution

It extends previous models to include two heat baths at different temperatures and a periodic force at any position, deriving new hydrodynamic equations with discontinuous slopes.

Findings

Derivation of a heat equation with a discontinuous slope at the force application point.

Extension of models to higher dimensions and anharmonic interactions.

Analysis of unpinned systems and their macroscopic behavior.

Abstract

We summarize and extend some of the results obtained recently for the microscopic and macroscopic behavior of a pinned harmonic chain, with random velocity flips at Poissonian times, acted on by a periodic force {at one end} and in contact with a heat bath at the other end. Here we consider the case where the system is in contact with two heat baths at different temperatures and a periodic force is applied at any position. This leads in the hydrodynamic limit to a heat equation for the temperature profile with a discontinuous slope at the position where the force acts. Higher dimensional systems, unpinned cases and anharmonic interactions are also considered.