Time-reversal symmetry breaking and odd viscosity in active fluids

Odd viscosity is a non-dissipative transport coefficient that appears in certain two-dimensional active fluids. We argue that the standard discussion of the connection of odd viscosity to time-reversal symmetry breaking involves a mistaken application of Onsager's reciprocal relations, and provide a derivation that circumvents this issue by directly applying Onsager's regression hypothesis. In doing so, we derive a Green-Kubo equation for the odd viscosity in terms of stress fluctuations. These are verified in a system of active dumbbells, thus supporting our application of the regression hypothesis to fluctuations about nonequilibrium steady states.

[1] Epstein, Mandadapu. "Time reversal symmetry breaking in two-dimensional non-equilibrium viscous fluids"

[2] Hargus, Klymko, Epstein, Mandadapu. "Time reversal symmetry breaking and odd viscosity in active fluids: Green–Kubo and NEMD results"