Heat Flow in a Periodically Forced, Thermostatted Chain II
Komorowski, Tomasz; Lebowitz, Joel; Olla, Stefano (2023), Heat Flow in a Periodically Forced, Thermostatted Chain II, Journal of Statistical Physics, 190, 87. 10.1007/s10955-023-03103-9
TypeArticle accepté pour publication ou publié
Journal nameJournal of Statistical Physics
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Abstract (EN)We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate γ. The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of n particles we compute the local temperature given by the expected value of the local energy and current. Scaling space and time diffusively yields, in the n → +∞ limit, the heat equation for the macroscopic temperature profile T (t, u), t > 0, u ∈ [0, 1]. It is to be solved for initial conditions T (0, u) and specified T (t, 0) = T − , the temperature of the left heat reservoir and a fixed heat flux J, entering the system at u = 1. J is the work done by the periodic force which is computed explicitly for each n.
Subjects / KeywordsPinned harmonic chain; Periodic force; Heat equation for the macroscopic temperature; Dirichlet-Neumann type boundary condition; Work into heat
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