Systematically elucidating the non-equilibrium steady states of active brownian particles

In equilibrium systems, the steady-state probability distribution (e.g., the Boltzmann distribution in the canonical ensemble) is known a priori. This is generally not true for non-equilibrium systems which can have non-vanishing currents. In this talk we demonstrate that one can perturbatively compute a steady-state probability distribution and an associated probability current for certain non-equilibrium systems, which then allows one to compute macroscopic averages in analogy to the equilibrium case. We apply this framework to a paradigmatic non-equilibrium system (active brownian particles in 2D) and compare our results with simulations. We demonstrate a quantitative agreement between our calculations and simulations for low enough Peclet number and average density.