The role of information flow in active matter

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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.