A Kac system interacting with two heat reservoirs
Abstract
We study a system formed by M particles moving in 3 dimension and interacting with 2 heat reservoirs with N>>M particles each. The system and the reservoirs evolve and interact via random collision described by a Kac-type master equation. The initial state of the reservoirs is given by 2 Maxwellian distributions at temperature T+ and T-. We show that, for times much shorter than N the interaction with the reservoirs is well approximated by the interaction with 2 Maxwellian thermostats, that is, heat reservoirs with N=∞. As a byproduct, if T+=T- we extend the results in BLTV to particles in 3 dimension.
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