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- W3165344765 abstract "We study a model of random colliding particles interacting with an infinite reservoir at fixed temperature and chemical potential. Interaction between the particles is modeled via a Kac master equation cite{kac}. Moreover, particles can leave the system toward the reservoir or enter the system from the reservoir. The system admits a unique steady state given by the Grand Canonical Ensemble at temperature $T=beta^{-1}$ and chemical potential $chi$. We show that any initial state converges exponentially fast to equilibrium by computing the spectral gap of the generator in a suitable $L^2$ space and by showing exponential decrease of the relative entropy with respect to the steady state. We also show propagation of chaos and thus the validity of a Boltzmann-Kac type equation for the particle density in the infinite system limit." @default.
- W3165344765 created "2021-06-07" @default.
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- W3165344765 date "2022-05-21" @default.
- W3165344765 modified "2023-09-23" @default.
- W3165344765 title "Grand Canonical Evolution for the Kac Model" @default.
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- W3165344765 doi "https://doi.org/10.1007/s10955-022-02932-4" @default.
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