A Kac system interacting with two heat reservoirs

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Bonetto, Federico, Loss, Michael, Powell, Matthew
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915945156444160
author Bonetto, Federico
Loss, Michael
Powell, Matthew
author_facet Bonetto, Federico
Loss, Michael
Powell, Matthew
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_13122
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Kac system interacting with two heat reservoirs
Bonetto, Federico
Loss, Michael
Powell, Matthew
Mathematical Physics
Statistical Mechanics
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.
title A Kac system interacting with two heat reservoirs
topic Mathematical Physics
Statistical Mechanics
url https://arxiv.org/abs/2508.13122