The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using two examples.

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具有非保守相互作用的硬粒子动力学的刘维尔方程的推导

刘维尔方程在推导物理系统的连续模型中具有根本重要性，这些模型由相互作用的粒子近似。然而，当粒子发生瞬时相互作用（例如碰撞）时，必须调整刘维尔方程的推导以排除非物理粒子位置，并包括瞬时相互作用的影响。我们提出了具有一般粒子动力学和相互作用的相互作用粒子的刘维尔方程的弱公式，并使用两个例子讨论了结果。