Ehrenfest relations at the glass transition: solution to an old paradox

TL;DR

This paper revisits Ehrenfest relations at the glass transition, clarifying their validity and proposing a thermodynamic framework for non-ergodic systems, including spin glasses and glass-forming liquids.

Contribution

It provides a corrected understanding of Ehrenfest relations at the glass transition and introduces thermodynamic relations for non-ergodic systems with a one-level phase space.

Findings

Ehrenfest relation involving compressibility is always satisfied.

The relation involving specific heat is generally incorrect.

A modified second Ehrenfest relation includes configurational entropy contributions.

Abstract

In order to find out whether there exists a thermodynamic description of the glass phase, the Ehrenfest relations along the glass transition line are reconsidered. It is explained that the one involving the compressibility is always satisfied, and that the one involving the specific heat is principally incorrect. Thermodynamical relations are presented for non-ergodic systems with a one-level tree in phase space. They are derived for a spin glass model, checked for other models, and expected to apply, e.g., to glass forming liquids. The second Ehrenfest relation gets a contribution from the configurational entropy.