Transport phenomena and Green-Kubo relations in active media: Theory

We derive Green-Kubo relations for the several viscosity terms that appear in a constitutive theory of viscous active fluids with and without an internal spin degree of freedom, starting from an Onsager regression hypothesis on the non-equilibrium steady state. In particular, we focus on the connection between time-reversal symmetry breaking and the emergence of the non-dissipative component of viscosity known as odd viscosity. Our results allow measurement of this odd viscosity in molecular dynamics simulations (for details see the corresponding Simulation talk). Time permitting, extensions of our results to liquid crystals will be discussed, with possible relevance to the modeling of active fluids such as suspensions or colonies of bacteria.

REF: Epstein and Mandadapu, Time reversal symmetry breaking in two-dimensional non-equilibrium viscous fluids