Isomorph theory of physical aging

TL;DR

This paper develops a theoretical framework using isomorph theory to describe the physical aging of R-simple systems, introducing the systemic temperature as a key parameter and predicting aging behavior under various thermodynamic jumps.

Contribution

It derives a configuration-space Langevin equation for aging R-simple systems and introduces the systemic temperature as a novel concept for describing non-equilibrium states.

Findings

Aging follows a specific phase diagram traced by density and systemic temperature.

Predicts aging behavior after density-temperature and pressure-temperature jumps.

R-simple liquids have a dynamic Prigogine-Defay ratio of unity.

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.