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We study some statistical properties for the behavior of the average squaredvelocity -- hence the temperature -- for an ensemble of classical particlesmoving in a billiard whose boundary is time dependent. We assume the collisionsof the particles with the boundary of the billiard are inelastic leading theaverage squared velocity to reach a steady state dynamics for large enoughtime. The description of the stationary state is made by using two differentapproaches: (i) heat transfer motivated by the Fourier law and, (ii) billiarddynamics using either numerical simulations and theoretical description.

Thermodynamics of a time dependent and dissipative oval billiard: a heat transfer and billiard approach