Article Dans Une Revue Electronic Journal of Probability Année : 2025

Heat flow in a periodically forced, unpinned thermostatted chain

Résumé

We prove the hydrodynamic limit for a one-dimensional harmonic chain of interacting atoms with a random flip of the momentum sign. The system is open: at the left boundary it is attached to a heat bath at temperature T_, while at the right endpoint it is subject to an action of a force which reads as $F + n^{-1/2}F̃(n^2 t)$, where F ⩾ 0 and F̃(t) is a periodic function. Here n is the size of the microscopic system. Under a diffusive scaling of space-time, we prove that the empirical profiles of the two locally conserved quantities – the volume stretch and the energy – converge, as n → +∞, to the solution of a non-linear diffusive system of conservative partial differential equations with a Dirichlet type and Neumann boundary conditions on the left and the right endpoints, respectively.

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Dates et versions

hal-04614909 , version 1 (17-06-2024)
hal-04614909 , version 2 (25-03-2025)

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Tomasz Komorowski, Stefano Olla, Marielle Simon. Heat flow in a periodically forced, unpinned thermostatted chain. Electronic Journal of Probability, 2025, 30 (66), pp.1-48. ⟨10.1214/25-EJP1326⟩. ⟨hal-04614909v2⟩
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