Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles†
The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion force f0 and a persistence time τp. Using the extended MCT and a generalized fluctuation–dissipation theorem, we calculate the effective temperature Teff of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent Teff that approaches a constant in the long-time limit, which depends on the activity parameters f0 and τp. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that τα, the α-relaxation time, behaves as τα ∼ f0−2γ, where γ = 1.74 is the MCT exponent for the passive system. τα may increase or decrease as a function of τp depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent γ. Comparison with the numerical solution of the nonequilibrium MCT and simulation results give excellent agreement with scaling analysis.