Isomorph theory of physical aging

Abstract

This paper derives and discusses the configuration-space Langevin equation describing a physically aging R-simple system and the corresponding Smoluchowski equation. Externally controlled thermodynamic variables like temperature, density, pressure enter the description via the single parameter ${T}_{\rm s}/T$ in which $T$ is the bath temperature and ${T}_{\rm s}$ is the "systemic" temperature defined at any time $t$ as the thermodynamic equilibrium temperature of the state point with density $\rho(t)$ and potential energy $U(t)$. In equilibrium ${T}_{\rm s}\cong T$ with fluctuations that vanish in the thermodynamic limit. In contrast to Tool's fictive temperature and other effective temperatures in glass science, the systemic temperature is defined for any configuration with a well-defined density, even if it is not in any sense close to equilibrium. Density and systemic temperature define an aging phase diagram in which the aging system traces out a curve. Predictions are discussed for aging following various density-temperature and pressure-temperature jumps from one equilibrium state to another, as well as for a few other scenarios. The proposed theory implies that R-simple glass-forming liquids are characterized by a dynamic Prigogine-Defay ratio of unity.