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''. 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.