Effective Temperature in Athermal Systems Sheared at Fixed Normal Load

We perform molecular dynamics simulations of repulsive athermal systems sheared at fixed normal load to study the effective temperature T_L defined from time-dependent fluctuation-dissipation relations for density. We show that these systems possess two distinct regimes as a function of the ratio T_S/V of the granular temperature to the potential energy per particle. At small T_S/V, these systems are pressure controlled and T_L is set by the normal load. In contrast, they behave as quasiequilibrium systems with T_L≈T_S that increases with the shear rate at large T_S/V. These results point out several problems with using T_L in thermodynamic descriptions of slowly sheared athermal systems.