开放系统n粒子分布函数的Liouville型方程
Liouville-type equations for the n-particle distribution functions of an open system
摘要：
在这项工作中，我们推导出一个数学模型的开放系统，交换粒子和动量与水库从他们的联合哈密顿动力学。这个多粒子问题的复杂性是通过引入一组可数的n粒子相空间分布函数只为开放的子系统，而占水库的统计预期。从刘维尔方程的完整系统，我们推导出一组耦合刘维尔型方程的n粒子分布的边缘化相对于水库状态。由此产生的方程层次描述了外部动量强迫的开放系统的水库跨越其边界，它涵盖了粒子交换的影响，诱导概率转移之间的n-和（n+1）-粒子分布。与开放系统的Bergmann-Lebowitz模型的异同（P.G.Bergmann，J.L. Lebowitz，Phys.Rev.，99：578- 587（1955））在分子模拟的计算方案中实施这些指导原则的背景下进行了讨论。
英文摘要：
In this work we derive a mathematical model for an open system that exchanges particles and momentum with a reservoir from their joint Hamiltonian dynamics. The complexity of this many-particle problem is addressed by introducing a countable set of n-particle phase space distribution functions just for the open subsystem, while accounting for the reservoir only in terms of statistical expectations. From the Liouville equation for the full system we derive a set of coupled Liouville-type equations for the n-particle distributions by marginalization with respect to reservoir states. The resulting equation hierarchy describes the external momentum forcing of the open system by the reservoir across its boundaries, and it covers the effects of particle exchanges, which induce probability transfers between the n- and (n+1)-particle distributions. Similarities and differences with the Bergmann-Lebowitz model of open systems (P.G.Bergmann, J.L. Lebowitz, Phys.Rev., 99:578--587 (1955)) are discussed in the context of the implementation of these guiding principles in a computational scheme for molecular simulations.
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