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Heat Flow in a Periodically Forced, Thermostatted Chain

Komorowski, Tomasz; Lebowitz, Joel L.; Olla, Stefano (2023), Heat Flow in a Periodically Forced, Thermostatted Chain, Communications in Mathematical Physics, 400, p. 2181–2225. 10.1007/s00220-023-04654-4

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Type
Article accepté pour publication ou publié
Date
2023
Journal name
Communications in Mathematical Physics
Number
400
Publisher
Springer
Pages
2181–2225
Publication identifier
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Author(s)
Komorowski, Tomasz
Polish Academy of Sciences (POLAND)
Lebowitz, Joel L.
Rutgers, The State University of New Jersey [New Brunswick] [RU]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We investigate the properties of a harmonic chain in contact at one end with a thermal bath and subjected at its other end to a periodic force. The particles also undergo a random velocity reversal action, which results in a finite heat conductivity of the system. We prove the approach of the system to a time periodic state and compute the heat current, equal to the time averaged work done on the system, in that state. This work approaches a finite positive value as the length of the chain increases. Rescaling space, the strength and/or the period of the force leads to a macroscopic temperature profile corresponding to the stationary solution of a continuum heat equation with Dirichlet-Neumann boundary conditions.