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Article Dans Une Revue Journal of Statistical Physics Année : 2023

HEAT FLOW IN A PERIODICALLY FORCED, THERMOSTATTED CHAIN II

Résumé

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.
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Dates et versions

hal-03793711 , version 1 (01-10-2022)
hal-03793711 , version 2 (23-04-2023)

Identifiants

Citer

Tomasz Komorowski, Joel L. Lebowitz, Stefano Olla. HEAT FLOW IN A PERIODICALLY FORCED, THERMOSTATTED CHAIN II. Journal of Statistical Physics, 2023, 190 (4), pp.87. ⟨10.1007/s10955-023-03103-9⟩. ⟨hal-03793711v1⟩
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