Configurational temperature in active matter. II. Quantifying the deviation from thermal equilibrium

This paper proposes using the configurational temperature T_{conf} for quantifying how far an active-matter system is from thermal equilibrium. We measure this "distance" by the ratio of the systemic temperature T_{s} to T_{conf}, where T_{s} is the canonical-ensemble temperature for which the average potential energy is equal to that of the active-matter system. T_{conf} is "local" in the sense that it is the average of a function, which depends only on how the potential energy varies in the vicinity of a given configuration. In contrast, T_{s} is a global quantity. The quantity T_{s}/T_{conf} is straightforward to evaluate in a computer simulation; equilibrium simulations in conjunction with a single steady-state active-matter configuration are enough to determine T_{s}/T_{conf}. We validate the suggestion that T_{s}/T_{conf} quantifies the deviation from thermal equilibrium by data for the radial distribution function of the 3D Kob-Andersen and 2D Yukawa active-matter models with active Ornstein-Uhlenbeck and active Brownian Particle dynamics. Moreover, we show that T_{s}/T_{conf}, structure, and dynamics of the homogeneous phase are all approximately invariant along the motility-induced phase separation boundary in the phase diagram of the 2D Yukawa model. The measure T_{s}/T_{conf} is not limited to active matter and can be used for quantifying how far any system involving a potential-energy function, e.g., a driven Hamiltonian system, is from thermal equilibrium.