The role of information flow in active matter

生物和人工活动系统，如细菌、机器人、鸟类或行人，显示出从个体到集体系统的有趣动态，在这些系统中，出现了自组织状态，如群集和羊群。由于能量从“燃料”源（例如ATP）持续转化为持续运动，这样的系统自然地远离热平衡运行，因此它们的理论描述提出了重大挑战。最近，有相当大的兴趣在描述主动系统的随机热力学，特别是在测量时间反演对称性破缺的个别轨迹的波动熵产生。重要的开放问题是链接的熵产生的基本散热和“热力学成本”的“活动”，并连接这种措施的不可逆性在不同层次的粗粒化。例如，最近的研究旨在制定一个热力学的水平上的随机流体动力场方程。然而，除了能量转换之外，主动和被动系统之间还有更重要的差异，例如感知，交流，记忆和反应的能力。尽管这些特征与个体和集体动力学有着明显的相关性，但对活性物质中信息交换的研究仍处于起步阶段。在这一建议中，我们的目的是提出我们的一般理解的作用，信息流的积极事项。第二个中心目标是将信息流与热力学原理联系起来。我们的想法是使用信息热力学理论先前建立的系统进行反馈控制。事实上，众所周知，只有考虑到信息论的量，总熵产生和系统的热耗散受到反馈可以相互联系，即在广义第二定律的形式。在这里，我们的目标是类似地推导出广义的第二定律的活性物质，包含连续的信息流之间的环境和活性粒子，或在一个集体的单个粒子。为了增加我们的调查的一般性，我们考虑一个单一的主动游泳者，一个基于粒子的系统，许多相互作用的游泳者，和一个流体动力场模型的集体主动系统。使用这些模型，我们想研究什么样的信息流发生，它们有什么方向，我们想证明这个量是一个一致的热力学描述的难题的重要组成部分。具体来说，我们的目标是调查“蜂拥”，“图案形成”，当地的熵产生和所产生的本地信息流之间的关系。

Living and artificial active systems, such as bacteria, robots, birds, or pedestrians, display intriguing dynamics from individual to collective systems, where self-organised states like swarms and flocks occur. Due to the ongoing conversion of energy from a ‘fuel’ source (e.g. ATP) into persistent motion, such systems naturally operate far from thermal equilibrium and their theoretical description therefore poses major challenges. Recently, there is considerable interest in describing active systems by means of stochastic thermodynamics, specifically, in measuring time-reversal symmetry breaking of individual trajectories by the fluctuating entropy production. Important open problems are to link the entropy production to the underlying heat dissipation and ‘thermodynamic cost’ of the ‘activity’, and to link this measure of irreversibility on different levels of coarse-graining. For example, recent research aims to formulate a thermodynamics on the level of stochastic hydrodynamic field equations. However, in addition to the energy-conversion, there are further crucial differences between active and passive systems, such as the abilities to perceive, communicate, remember, and react. Despite the obvious relevance of these features for the individual and collective dynamics, the study of information exchange in active matter is still in its infancy. In this proposal, we aim to put forward our general understanding of the role of information flow for active matter. The second central goal is to connect the information flow to thermodynamic principles. Our idea is to use the theory of information-thermodynamics previously established for systems subject to feedback control. Indeed, it is well-known that only by taking into account information-theoretic quantities, the total entropy production and the heat dissipation of systems subject to feedback can be linked with each other, namely in the form of generalised second laws. Here we aim to analogously derive generalised second laws for active matter, containing the continuous information flow between environment and active particle, or between individual particles in a collective. To increase the generality of our investigations, we consider a single active swimmer, a particle-based system of many interacting swimmers, and a hydrodynamic field model of a collective active system. Using these models, we want to investigate what kind of information flows occur, what direction they have, and we want to demonstrate that this quantity is an important piece of the puzzle of a consistent thermodynamic description. Specifically, we aim to investigate the relation between ‘swarming’, ‘pattern formation’, local entropy production and the arising local information flows.