Work extraction from active matter systems

This thesis examines active matter, a particular class of non-equilibrium systems consisting of agents that autonomously extract energy from their surroundings to sustain their dynamics. Examples include biological systems, such as molecular motors and bacteria, as well as synthetic counterparts, such as Janus particles. Active matter defies "equilibrium" thermodynamics by breaking the principle of detailed balance. While this renders much of the standard statistical mechanics toolkit ineffective, the upside is that it leads to a rich array of phenomena with no equilibrium counterpart. Perhaps the most familiar is the ability of active matter to spontaneously perform useful work. With growing interest in this phenomenon, I explore how active matter can be modelled and leveraged to perform useful work, especially in the context of "active engines", i.e. microscale machines powered by active matter. This thesis comprises two main parts. The first presents various minimal models of work extraction from active particles. These demonstrate how particle currents can be channelled to perform work, while also considering key concepts like autonomy and efficiency. These models roughly increase in complexity as the chapters progress, culminating in the design of a protocol that extracts optimal power from active particles with hidden internal states. The next part addresses the role of dense active matter in the development of active engines. I characterise one such class of dense active matter, namely active crystals, through exact calculations of its thermodynamic properties, including fluctuations, energy, and entropy production. I also investigate foundational principles, such as how activity affects the crystalline order of these regularly arranged condensates. Aside from providing insight into the fundamental properties of active matter, the framework presented in this thesis is easily extensible to more complex systems, and thus offers a pathway to harnessing the unique properties of active matter for practical use.