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Hydrodynamic limit for a chain with thermal and mechanical boundary forces

Abstract : We prove the hydrodynamic limit for an harmonic chain with a random exchange of momentum that conserves the kinetic energy but not the momentum. The system is open and subject to two thermostats at the boundaries and to external tension. 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 to the solution of a non-linear diffusive systems of conservative partial differential equations.
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https://hal.inria.fr/hal-02538469
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Submitted on : Saturday, April 18, 2020 - 3:53:49 PM
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Tomasz Komorowski, Stefano Olla, Marielle Simon. Hydrodynamic limit for a chain with thermal and mechanical boundary forces. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2021, 26, ⟨10.1214/21-EJP581⟩. ⟨hal-02538469v2⟩

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