Decay of Information for the Kac Evolution

We consider a system of $M$ particles in contact with heat reservoir $N\gg M$ particles. The evolution the and reservoir, together their interaction, are modeled via Kac's Master Equation. chose initial distribution total energy $N+M$ show that if is initially equilibrium, depends only on particle then entropy decay exponentially to very small value. base our proof similar property for Information. A argument allows us greatly simplify main result [2].