Isomorph theory of physical aging.
This paper derives and discusses the Langevin equation describing a physically aging R-simple system and the corresponding Smoluchowski equation. Externally controlled thermodynamic variables (temperature, density, pressure) enter the description via the single parameter $\Teq/T$ in which $T$ is the bath temperature and $\Teq$ 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 $\Teq\cong T$ with fluctuations that vanish in the thermodynamic limit. Density and systemic temperature define an "aging phase diagram" in which the system traces out a curve. In contrast to Tool's fictive temperature and other effective temperatures in glass science, the systemic temperature is defined for any configuration, also if it is not in any sense close to equilibrium. The proposed theory implies that R-simple glass-forming liquids are characterized by a unity dynamic Prigogine-Defay ratio [N. L. Ellegaard et al., J. Chem. Phys. 126, 074502 (2007)]. 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 aging scenarios.
Publisher URL: http://arxiv.org/abs/1801.06890
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