Ratio of effective temperature to pressure controls the mobility of sheared hard spheres

Using molecular dynamics simulations, we calculate fluctuations and responses for steadily sheared hard spheres over a wide range of packing fractions phi and shear strain rates (gamma) over dot, using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature T-eff that is equal to or larger than the kinetic temperature T-kin. We find a crossover in the relationship between the relaxation time tau and the the nondimensionalized effective temperature T-eff/p sigma(3), where p is the pressure and sigma is the sphere diameter. In the solid response regime, the behavior at a fixed packing fraction satisfies tau(gamma) over dot alpha exp(-cp sigma(3)/T-eff), where c depends weakly on phi suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on T-eff/p sigma(3) as it depends on T-kin/p sigma(3) in equilibrium. This regime includes both near-equilibrium conditions where T-eff similar or equal to T-kin and far-from-equilibrium conditions where T-eff not equal T-kin. We discuss the implications of our results for systems with soft repulsive interactions.