Phase Transition in the Boltzmann–Vlasov Equation

In this paper we revisit the problem of explaining phase transition by a study of a form of the Boltzmann equation, where inter-molecular attraction is included by means of a Vlasov term in the evolution equation for the one particle distribution function. We are able to show that for typical gas de...

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Bibliographic Details
Published in:Journal of statistical physics 2019-01, Vol.174 (5), p.1011-1026
Main Author: Fowler, A. C.
Format: Article
Language:English
Subjects:
Analysis
Attraction
Boltzmann transport equation
Distribution functions
Mathematical analysis
Mathematical and Computational Physics
Phase transitions
Physical Chemistry
Physics
Physics and Astronomy
Probability distributions
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Variation
Vlasov equations
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Summary:In this paper we revisit the problem of explaining phase transition by a study of a form of the Boltzmann equation, where inter-molecular attraction is included by means of a Vlasov term in the evolution equation for the one particle distribution function. We are able to show that for typical gas densities, a uniform state is unstable if the inter-molecular attraction is large enough. Our analysis relies strongly on the assumption, essential to the derivation of the Boltzmann equation, that ν ≪ 1 , where ν = d / l is the ratio of the molecular diameter to the mean inter-particle distance; in this case, for fluctuations on the scale of the molecular spacing, the collision term is small, and an explicit approximate solution is possible. We give reasons why we think the resulting approximation is valid, and in conclusion offer some possibilities for extension of the results to finite amplitude.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-019-02222-6