Hydrodynamic limit for a chain with thermal and mechanical boundary forces

Tomasz Komorowski (1) , Stefano Olla (2) , Marielle Simon (3)

1 PAN - Institut of Mathematics - Polish Academy of Sciences
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Paradyse - Systèmes de particules et systèmes dynamiques

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.

Mots clés: Boundary conditions; Fourier-Wigner functions; Harmonic chain; Hydrodynamic limit

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]

Tomasz Komorowski, Stefano Olla, Marielle Simon. Hydrodynamic limit for a chain with thermal and mechanical boundary forces. Electronic Journal of Probability, 2021, 26, ⟨10.1214/21-EJP581⟩. ⟨hal-02538469v2⟩