Effective Temperatures in Athermal Systems Sheared at Fixed Normal Load

TL;DR

This study uses molecular dynamics simulations to explore how effective temperature behaves in sheared athermal systems under fixed normal load, revealing two distinct regimes based on the ratio of granular temperature to potential energy.

Contribution

It demonstrates the existence of two regimes of effective temperature in sheared athermal systems and highlights limitations of using effective temperature in thermodynamic descriptions.

Findings

At low T_S/V, T_L is pressure-controlled by normal load.

At high T_S/V, T_L approximates T_S and increases with shear rate.

The study identifies problems with using T_L in thermodynamic models.

Abstract

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 quasi-equilibrium systems with $T_L \approx T_S$ that increases with 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.