  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.
