Active thermodynamics of inertial chiral active gases: Equation of state and edge currents

One of the most fundamental quests in the physics of active matter concerns the existence of a comprehensive theory for its macroscopic properties, i.e. an "active thermodynamics." Recently, despite progress in developing this field, crucial questions, such as the influence of chirality on the thermodynamics of active matter, remain open-even in the simplest and most generic case of the ideal active gas. Here, we derive and experimentally verify key elements of the active thermodynamics of ideal chiral active gases, unveiling edge currents and odd diffusivity as their peculiar features. Our main results are the derivation of an equation of state relating density and pressure via a chirality-dependent effective temperature, the derivation of Fick's law, including the full diffusion matrix predicting odd diffusion, and the exact prediction of edge currents at container walls that nonmonotonically depend on chirality. Our results serve as a crucial step toward a comprehensive understanding of how chirality influences and allows us to control the macroscopic properties of active matter.