The mechanics of Fick’s Law and odd diffusion

Fick's Law posits a linear relationship between diffusive fluxes and density gradients. These fluxes are usually oriented down density gradients, causing matter to "spread out". Odd diffusion, however, generates fluxes orthogonal to density gradients, and is a direct consequence of broken time-reversal symmetry (TRS) at the level of individual particles. As such, it is a common feature of chiral active matter. The connection between macroscopic odd diffusion and TRS-breaking in the spontaneous fluctuations about the steady state is made quantitative through Green-Kubo relations, which hold even in systems such as active matter where the steady state is inherently out of equilibrium. In this talk we highlight a further mechanical connection between odd diffusion and the antisymmetric hydrostatic stress, which is the part of the stress arising due to microscopic (e.g. active) torques. We show that this mechanical relationship determines the exact form of the odd diffusivity for a model fluid composed of actively-torqued dumbbell particles, even when the torques are large and when the density of dumbbells is high.