A Rigorous Derivation of the Entropy Bound and the Nature of Entropy Variation for Non-equilibrium Systems during Cooling

TL;DR

This paper rigorously proves bounds on the residual entropy of non-equilibrium systems during cooling, showing it cannot fall below the equilibrium entropy, and clarifies the statistical interpretation of thermodynamic entropy.

Contribution

It provides a rigorous thermodynamic derivation of entropy bounds for non-equilibrium systems, extending previous calorimetric observations to all such systems.

Findings

Residual entropy is bounded below by the equilibrium entropy.

Instantaneous entropy cannot be lower than the equilibrium state.

Gibbs and Boltzmann interpretations are valid for single samples.

Abstract

We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the entropy of the corresponding equilibrium (metastable supercooled liquid) state, and (ii) the instantaneous entropy cannot drop below that of the equilibrium state. The theorems follow from the second law and the existence of internal equilibrium and refer to the thermodynamic entropy. They go beyond the calorimetric observations by Johari and Khouri [J. Chem. Phys. 134, 034515 (2011)] and others by extending them to all non-equilibrium systems regardless of how far they are from their equilibrium states. We also discuss the statistical interpretation of the thermodynamic entropy and show that the conventional Gibbs or Boltzmann interpretation gives the correct thermodynamic entropy even for a single sample regardless of the duration of measurements.