title: Collective Behavior in Inertial Active Matter
Creators: name: Hecht, Lukas
Publisher: name: UNSPECIFIED
Year: 2024

description: Active matter consists of particles which consume energy to convert it into directed motion. Due to this local energy conversion, active matter is intrinsically out of equilibrium. This manifests in striking collective phenomena. For example, active particles can phase separate into a dense and a dilute phase without any attractive interactions by motility-induced phase separation, or they can form stationary or moving patterns. In stark contrast to systems in thermodynamic equilibrium, active particles can even self-assemble into clusters in which they feature a persistently lower kinetic temperature, i.e., mean kinetic energy, compared to particles in their environment. This phenomenon requires inertia and raises the general question of how inertia influences collective behavior in active matter. In particular, the influence of inertia on the emergence of coexisting temperatures is not fully understood. More generally, it is under debate how to define temperature in an active system at all. The aim of this thesis is to provide fundamental insights into these questions. As a key non-equilibrium phenomenon, we explore the emergence of coexisting temperatures in inertial active Brownian particles, which undergo motility-induced phase separation, by using Brownian dynamics simulations. First, we show that the effect of inertia on the phase transition line and the emergence of coexisting kinetic temperatures allows designing a mechanism of a "refrigerator" for active particles. Without requiring any isolating walls, it is able to decrease their kinetic temperature by two orders of magnitude compared to the environment. Second, we observe coexisting kinetic temperatures even in mixtures of overdamped active and inertial passive particles, when they undergo motility-induced phase separation. We show that the liquid-like phase can be not only colder but also hotter than the gas-like phase. Finally, we show that these results are robust against the used "thermometer". In particular, we compare different possibilities to calculate temperature in active systems by applying well-established thermodynamic relations. This comparison yields the existence of two temperature classes. In both classes, we identify methods that are independent of tracer properties or external confinements, and hence, are suited for measuring the temperature of active matter. We further investigate control mechanisms for particle self-assembly by developing a minimal model for assembling colloidal particles in the trail of an ion-exchange resin bead. Our simulations describe the experiments well, both qualitatively and quantitatively. The numerical investigation of the explored systems requires a wide range of data analysis tools. Thus, we developed the Active Matter Evaluation Package for the analysis of the simulation data. This Python library allows for quickly calculating observables which provide insights into the structural and dynamical properties of the investigated systems. It is the first tool that is specifically designed for the analysis of active matter systems. The results of this thesis provide routes to control self-assembly and temperature in active systems, and the detailed comparison of different temperature definitions can serve as a starting point towards a thermodynamic theory for active matter. The explored colloidal self-assembly could be applied as a new technique to write lines and letters into water, and finally, the developed Python library is publicly available as open-source software and provides essential tools to study phase separation, pattern formation, and critical phenomena in active matter systems and beyond.