Isomorph theory beyond thermal equilibrium

Abstract

This paper generalizes isomorph theory to systems that are not in thermal equilibrium. The systems are assumed to be R-simple, i.e., have a potential energy that as a function of all particle coordinates R obeys the hidden-scale-invariance condition U (Ra) < U (R b ) ⇒ U (λRa) < U (λR b ). Generalized "systemic" isomorphs are lines of constant excess entropy in the phase diagram defined by density and systemic temperature, which is the temperature of the equilibrium state point with average potential energy equal to U (R). In thermal equilibrium, the systemic temperature is the bath temperature and the equilibrium isomorph formalism is recovered. The new approach rationalizes within a consistent framework previously published observations of isomorph invariance in simulations involving steady-state shear flow, zero-temperature plastic flows, and glass-state isomorphs. The paper relates also briefly the non-equilibrium isomorph formalism to physical aging, active matter, and granular media. It is proposed that for any steady-state R-simple system the effective temperature characterizing fluctuation-dissipation-theorem violations is identical to the systemic temperature. Finally, we discuss the possibility that the energy unit defining reduced quantities should be based on the systemic temperature instead of the bath temperature, as is currently the case.