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arXiv · 2508.13122

A Kac system interacting with two heat reservoirs

Federico Bonetto·Michael Loss·Matthew Powell
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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 $\sqrt{N}$ the interaction with the reservoirs is well approximated by the interaction with 2 Maxwellian thermostats, that is, heat reservoirs with $N=\infty$. As a byproduct, if $T_+=T_-$ we extend the results in \cite{BLTV} to particles in 3 dimension.

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Federico Bonetto, Michael Loss, Matthew Powell. 2025-08-18. A Kac system interacting with two heat reservoirs. https://arxiv.org/abs/2508.13122

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