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1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision 2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Abstract : We obtain macroscopic adiabatic thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics subject to random collisions with the environment. The microscopic dynamics is given by a chain of oscillators subject to a varying tension external force and to collisions with external independent particles of -infinite mass-. The effect of each collision is to change the sign of the velocity without changing the modulus. This way the energy is conserved by the resulting dynamics. After a diffusive space-time scaling and cross-graining, the profiles of volume and energy converge to the solution of a deterministic diffusive system of equations with boundary conditions given by the applied tension. This defines an irreversible thermodynamic transformation from an initial equilibrium to a new equilibrium given by the final tension applied. Quasi-static reversible adiabatic transformations are then obtained by a further time scaling. Then we prove that the relations between the limit work, internal energy and thermodynamic entropy agree with the first and second principle of thermodynamics.

Keywords : Adiabatic thermodynamic transformations thermodynamic entropy hydrodynamic limit quasi static trasformations

Author: Stefano Olla - Marielle Simon -

Source: https://hal.archives-ouvertes.fr/


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