Year: 2026
Type: article
Abstract: We study a system formed by M particles moving in 3 dimension and interacting with 2 heat reservoirs with $$N>>M$$ 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 $$T_+$$ T + and $$T_-$$ T - . We show that, for times much shorter than $$\sqrt{N}/M$$ N / M the interaction with the reservoirs is well approximated by the interaction with 2 Maxwellian thermostats, that is, heat reservoirs with $$N=\infty $$ N = ∞ . As a byproduct, if $$T_+=T_-$$ T + = T - we extend the results in [3] to particles in 3 dimension.
Authors: Federico Bonetto, Michael Loss, Matthew Powell
Institution: Georgia Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Funder: National Science Foundation
OpenAlex ID: W4414528102
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