Abstract：
In the last decade, the thermostatted kinetic theory has been proposed as a general paradigm for the modeling of complex systems of the active matter and, in particular, in biology. Homogeneous and inhomogeneous frameworks of the thermostatted kinetic theory have been employed for modeling phenomena that are the result of interactions among the elements, called active particles, composing the system. Functional subsystems contain heterogeneous active particles that are able to perform the same task, called activity. Active matter living systems usually operate out-of-equilibrium; accordingly, a mathematical thermostat is introduced in order to regulate the fluctuations of the activity of particles. The time evolution of the functional subsystems is obtained by introducing the conservative and the nonconservative interactions which represent activity-transition, natural birth/death, induced proliferation/destruction, and mutation of the active particles. This review paper is divided in two parts: In the first part the review deals with the mathematical frameworks of the thermostatted kinetic theory that can be found in the literature of the last decade and a unified approach is proposed; the second part of the review is devoted to the specific mathematical models derived within the thermostatted kinetic theory presented in the last decade for complex biological systems, such as wound healing diseases, the recognition process and the learning dynamics of the human immune system, the hiding-learning dynamics and the immunoediting process occurring during the cancer-immune system competition. Future research perspectives are discussed from the theoretical and application viewpoints, which suggest the important interplay among the different scholars of the applied sciences and the desire of a multidisciplinary approach or rather a theory for the modeling of every active matter system.
摘要：
在过去的十年里，恒温动力学理论已被提出作为对活性物质的复杂系统进行建模的一般范例，特别是,在生物学中。恒温动力学理论的均质和不均匀框架已用于建模现象，这些现象是元素之间相互作用的结果。称为活性粒子，组成系统。功能子系统包含能够执行相同任务的异质活性粒子，称为活动。活性物质生命系统通常不平衡地运行；因此，引入了数学恒温器，以调节粒子活动的波动。通过引入代表活动过渡的保守和非保守相互作用来获得功能子系统的时间演化，自然出生/死亡，诱导增殖/破坏，和活性粒子的突变。这篇综述论文分为两部分：在第一部分中，综述涉及可以在过去十年的文献中找到的恒温动力学理论的数学框架，并提出了统一的方法；评论的第二部分致力于在过去十年中针对复杂的生物系统提出的恒温动力学理论中得出的特定数学模型，如伤口愈合疾病，人类免疫系统的识别过程和学习动态，在癌症-免疫系统竞争过程中发生的隐藏学习动力学和免疫编辑过程。从理论和应用的角度探讨了未来的研究视角，这表明应用科学的不同学者之间的重要相互作用，以及多学科方法或更确切地说是对每个活性物质系统进行建模的理论的愿望。
