Temperature of systems out of thermodynamic equilibrium

TL;DR

This paper demonstrates the equivalence of two phenomenological approaches to describing systems out of thermodynamic equilibrium, leading to a generalized concept of temperature applicable beyond glasses, encompassing any irreversible transformation.

Contribution

It establishes the equivalence of the fictive temperature and thermodynamic approaches, enabling a unified definition of effective temperature for all non-equilibrium systems.

Findings

Proves the equivalence of two approaches for glasses and general systems.

Defines an effective temperature for systems out of equilibrium.

Generalizes the fictive temperature concept beyond glasses.

Abstract

Two phenomenological approaches are currently used in the study of the vitreous state. One is based on the concept of fictive temperature introduced by Tool [Jour. Research Nat. Bur. Standards 34, 199 (1945)] and recently revisited by Nieuwenhuizen [Phys. Rev. Lett. 80, 5580 (1998)]. The other is based on the thermodynamics of irreversible processes initiated by De Donder at the beginning of the last century [L'Affinit\'e (Gauthier-Villars, Paris, 1927)] and recently used by M\"oller and co-workers for a thorough study of the glass transition [J. Chem. Phys. 125, 094505 (2006)]. This latter approach leads to the possibility of describing the glass transition by means of the freezing-in of one or more order parameters connected to the internal structural degrees of freedom involved in the vitrification process. In this paper, the equivalence of the two preceding approaches is demonstrated, not only for glasses, but in a very general way for any system undergoing an irreversible transformation. This equivalence allows the definition of an effective temperature for all systems departed from equilibrium generating a positive amount of entropy. In fact, the initial fictive temperature concept of Tool leads to the generalization of the notion of temperature for systems out of thermodynamic equilibrium, for which glasses are just particular cases.