Phase behavior and directed transport of active Brownian particles under extreme confinement

Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical phase behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions. In addition, we provide an analytical theory for computing transport coefficient under such confined conditions and derive expressions for the long and short-time self-diffusivity as a function of packing fraction and activity.