Towards a statistical mechanics of chiral active gases

Statistical mechanics allows to describe materials near equilibrium using just a few thermodynamic variables. Extending this approach far-from-equilibrium is tempting but often unfeasible. In this talk, we present the footprints of a statistical mechanical treatment of chiral active fluids composed of self-spinning particles. The nature of self-spinning breaks time-reversal symmetry and detailed balance. Nevertheless, such active fluids converge to a non-equilibrium steady state exhibiting Boltzmann statistics with a universal effective temperature determined by the active torques. Beyond exhibiting analogues of common thermodynamic properties, the chiral active gas also displays a dissipation-less odd viscosity in addition to the shear viscosity. Both transport coefficients satisfy a Kubo relation in terms of our effective temperature. We show that the stochastic dynamics of this many body system can be represented as a chiral Brownian motion in shear-stress space. Using this assumption, we derive analytically the full frequency dependence of the viscosities in agreement with simulations.