A Kac system interacting with two heat reservoirs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915945156444160 |
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| 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 |