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 φ and shear strain rates γ[over ̇], 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 τ and the the nondimensionalized effective temperature T(eff)/pσ(3), where p is the pressure and σ is the sphere diameter. In the solid response regime, the behavior at a fixed packing fraction satisfies τ ̇γ∝exp(-cpσ(3)/T(eff)), where c depends weakly on φ, 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)/pσ(3) as it depends on T(kin)/pσ(3) in equilibrium. This regime includes both near-equilibrium conditions where T(eff)≃T(kin) and far-from-equilibrium conditions where T(eff)≠T(kin). We discuss the implications of our results for systems with soft repulsive interactions.