Odd Viscodiffusive Fluids*

We present a class of materials termed "odd viscodiffusive fluids," which exhibit odd transport by coupling diffusive fluxes to concentration gradients and reciprocally, stresses to concentration gradients. While other odd transport phenomena, such as odd viscous dissipation and odd diffusion, are observed in chiral active systems, they are limited to two-dimensions. In contrast, we showcase odd viscodiffusive coupling to be an instance of odd transport in three-dimensions. By analyzing microscopic fluctuations in the steady state, we use the recently proposed "flux hypothesis" to develop Green-Kubo and reciprocal relations for the governing transport coefficients. These relations suggest that only parity symmetry, and not time-reversal symmetry, must be broken at the microscopic scale to observe these couplings, allowing for these materials to be either passive or active. We then discuss a few analytically tractable cases that illustrate the nature of viscodiffusive cross-coupling in chiral matter, and enable the experimental measurement of the novel transport coefficients. Finally, we make the case for chiral bacterial suspensions to be odd viscodiffusive fluids, and use our theory to understand prior experimental studies involving bacterial migration in response to shearing flows.