标题： 关于开放的活性软物质系统的运动方程 显示英文标题

标题： Towards kinetic equations of open systems of active soft matter

摘要： 本章介绍了一些描述基于可观测量（如开系统）演化方程的数学生物学复杂系统集体行为的新方法。 自传统意义上动力学理论中使用的状态概念更加微妙且是生物群体的隐含特征以来，这种动力学演化表示法似乎是建模生物系统集体行为最直接且在数学上完全一致的表述。 该方法的一个优势是可以构建开放复杂系统的动力学方程，在涉及初始关联的尺度近似中，特别是那些可以表征活性软物质凝聚态的关联。 此外，这种方法还涉及到从多实体动力学推导非马尔可夫动力学方程的挑战，这使得描述生物群体集体行为的记忆效应成为可能。 显示英文摘要

摘要： The chapter presents some new approaches to describing the collective behavior of complex systems of mathematical biology based on the evolution equations of observables such as open systems. This representation of kinetic evolution has looked to be the most direct and mathematically fully consistent formulation modeling the collective behavior of biological systems since the traditionally used concept of the state in kinetic theory is more subtle and is an implicit characteristic of the populations of living creatures. One of the advantages of the developed approach is the opportunity to construct kinetic equations for open complex systems in scaling approximations, involving initial correlations, in particular, that can characterize the condensed states of active soft matter. An approach is also related to the challenge of a rigorous derivation of the non-Markovian kinetic equations from underlying many-entity dynamics, which makes it possible to describe the memory effects of the collective behavior of living creatures.