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 $$\nu \ll 1,$$ν≪1, where $$\nu =d/l$$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.

中文翻译：

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Boltzmann-Vlasov 方程中的相变

在本文中，我们通过研究玻尔兹曼方程的一种形式重新审视解释相变的问题，其中分子间吸引力通过单粒子分布函数的演化方程中的 Vlasov 项包括在内。我们能够证明，对于典型的气体密度，如果分子间吸引力足够大，则均匀状态是不稳定的。我们的分析强烈依赖于推导玻尔兹曼方程必不可少的假设，即 $$\nu \ll 1,$$ν≪1，其中 $$\nu =d/l$$ν=d/l 是分子直径与平均颗粒间距离的比值；在这种情况下，对于分子间距尺度上的波动，碰撞项很小，并且可能有明确的近似解。我们给出我们认为所得近似值有效的原因，