Mesoscopic Description of the Adiabatic Piston: Kinetic Equations and H -Theorem
Abstract
The adiabatic piston problem is solved at the mesoscale using a kinetic theory approach. The problem is to determine the evolution towards equilibrium of two gases separated by a wall with only one degree of freedom (the adiabatic piston). A closed system of equations for the distribution functions of the gases conditioned to a position of the piston and the distribution function of the piston is derived, under the assumption of a generalized molecular chaos. It is shown that the resulting kinetic description has the canonical equilibrium as a steady-state solution. Moreover, the Boltzmann entropy, which includes the motion of the piston, verifies the
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- September 2019
- DOI:
- 10.1007/s10955-019-02336-x
- arXiv:
- arXiv:1903.01557
- Bibcode:
- 2019JSP...176.1138K
- Keywords:
-
- Adiabatic piston;
- Kinetic theory;
- Boltzmann equation;
- H$${\mathcal {H}}$$-theorem;
- 70Fxx;
- 82B40;
- 82C40;
- 82D05;
- Condensed Matter - Statistical Mechanics;
- Mathematical Physics;
- Physics - Fluid Dynamics
- E-Print:
- 25 pages, 2 figures