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

Komorowski, Tomasz; Lebowitz, Joel L.; Olla, Stefano; Simon, Marielle (2023), On the Conversion of Work into Heat: Microscopic Models and Macroscopic Equations, Ensaios Matemáticos, 38, p. 325-341. 10.21711/217504322023/em3812

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Type
Article accepté pour publication ou publié
Date
2023
Journal name
Ensaios Matemáticos
Volume
38
Publisher
Brazilian Mathematical Society
Pages
325-341
Publication identifier
Metadata
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Author(s)
Komorowski, Tomasz
Institut of Mathematics - Polish Academy of Sciences [PAN]
Lebowitz, Joel L.
Department of Mathematics - Rutgers School of Arts and Sciences
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Simon, Marielle
Institut Camille Jordan [ICJ]
Abstract (EN)
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.
Subjects / Keywords
Heat transfer; Periodic Forcing; Microscopic stochastic dynamics; Hydrodynamic Limits; Harmonic chain; Heat equation for the macroscopictemperature; Dirichlet-Neumann type boundary conditions; workinto heat