标题： 粒子数变化系统的动力学：从Liouville方程到开放系统的广义主方程 显示英文标题

标题： Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems

摘要： 系统中粒子数量的变化是自然界和技术系统中最相关的特征之一，从与周围环境的能量和物质交换到通过内部动力学（如反应）改变粒子数量。这些系统的物理数学建模极具挑战性，主要困难在于自由度数量的时间依赖性，以及粒子数量和种类的增加或减少必须不违反基本物理定律的额外约束。在这种情况下的理论模型是设计计算策略的关键工具，用于数值研究以获得可信的结果。在本文中，我们回顾了受不同具体数值目标启发的粒子数量变化的互补物理数学方法。通过对这些模型基础共同结构的分析，我们提出了一种统一的主方程，适用于具有变化粒子数量的一般动力系统。该方程包含了所有先前的模型，并有可能模拟更广泛的复杂系统，从分子到社会代理的基础动态。 显示英文摘要

摘要： A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we review complementary physico-mathematical approaches of varying number of particles inspired by rather different specific numerical goals. As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics.