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• W2004187585 abstract "The evolution of a homogeneous dilute gas is treated as a Markov process in the complete set of $K$ coarsegrained velocity states of all $N$ particles. From the Siegert master equation for the process a Fokker-Planck equation is derived which describes, in the limit $Nensuremath{rightarrow}ensuremath{infty}$, the fluctuations in the occupation numbers ${n}_{i}(t)$, whose average behavior is governed by the (appropriately discretized) Boltzmann equation: The continuum limit $Kensuremath{rightarrow}ensuremath{infty}$ corresponds to fluctuations in the usual molecular distribution function $f(stackrel{ensuremath{rightarrow}}{mathrm{r}}stackrel{ensuremath{rightarrow}}{mathrm{v}};t)$. On similar reasoning, a Fokker-Planck equation is obtained for the fluctuation process near equilibrium, where the average is governed by the linearized Boltzmann equation. The theory of linear irreversible processes, which offers a statistical description of fluctuations on a thermodynamical basis, is applied to the linearized Boltzmann equation---treated as a linear phenomenological equation---following the development given recently by Fox and Uhlenbeck: The resulting stochastic equation is seen to be equivalent to the Fokker-Planck equation obtained from the master equation, yielding a multidimensional Ornstein-Uhlenbeck process which describes the fluctuations in molecular phase space." @default.
• W2004187585 created "2016-06-24" @default.
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• W2004187585 date "1976-01-01" @default.
• W2004187585 modified "2023-10-16" @default.
• W2004187585 title "Fluctuations and the Boltzmann equation. I" @default.
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• W2004187585 doi "https://doi.org/10.1103/physreva.13.458" @default.
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