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On the Conversion of Work into Heat: Microscopic Models and Macroscopic Equations
Tomasz Komorowski, Joel Lebowitz, Stefano Olla, Marielle Simon · 2022-12-01 · via math.PR updates on arXiv.org

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.

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