Hierarchy of Relaxation times and Residual Entropy: A Nonequilibrium Approach

TL;DR

This paper develops a nonequilibrium thermodynamics framework for supercooled liquids and glasses using internal variables classified by relaxation times, providing bounds on residual entropy and insights into entropy relaxation.

Contribution

It introduces a hierarchy-based classification of internal variables and derives bounds on residual entropy, clarifying the role of inactive variables in nonequilibrium thermodynamics.

Findings

Bound on residual entropy established

Inactive variables influence temperature and pressure deviations

Entropy loss theories are shown to be inconsistent with the second law

Abstract

We consider nonequilibrium (NEQ) states such as supercooled liquids and glasses that are described with use of internal variables. We classify the latter by state-dependent hierarchy of relaxation times to assess their relevance for irreversible contributions. Given an observation time {\tau}_{obs}, we determine the window of relaxation times that divide the internal variables into active and inactive groups, the former playing a central role in the NEQ thermodynamics. Using this thermodynamics, we determine (i) a bound on the NEQ entropy and on the residual entropy, and (ii) the nature of isothermal relaxation of the entropy and the enthalpy in accordance with the second law. A theory that violates the second law such as the entropy loss view is shown to be internally inconsistent if we require it to be consistent with experiments. The inactive internal variables still play an indirect role in determining the temperature T(t), the pressure P(t), of the system, which deviate from their external values.