Thermodynamics of a time dependent and dissipative oval billiard: a heat   transfer and billiard approach
  We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the particles with the boundary of the billiard are inelastic leading the average squared velocity to reach a steady state dynamics for large enough time. The description of the stationary state is made by using two different approaches: (i) heat transfer motivated by the Fourier law and, (ii) billiard dynamics using either numerical simulations and theoretical description. 
Edson D. Leonel, Marcus Vinicius Camillo Galia, Luiz Antonio Barreiro,   Diego F. M. Oliveira
nlin.CD