  We present a thermodynamic theory of the Kovacs effect based on the idea that
the configurational degrees of freedom of a glass-forming material are driven
out of equilibrium with the heat bath by irreversible thermal contraction and
expansion. We assume that the slowly varying configurational subsystem, i.e.
the part of the system that is described by inherent structures, is
characterized by an effective temperature, and contains a volume-related
internal variable. We examine mechanisms by which irreversible dynamics of the
fast, kinetic-vibrational degrees of freedom can cause the entropy and the
effective temperature of the configurational subsystem to increase during
sufficiently rapid changes in the bath temperature. We then use this theory to
interpret the numerical simulations by Mossa and Sciortino (MS), who observe
the Kovacs effect in more detail than is feasible in laboratory experiments.
Our analysis highlights two mechanisms for the equilibration of internal
variables. In one of these, an internal variable first relaxes toward a state
of quasi-equilibrium determined by the effective temperature, and then
approaches true thermodynamic equilibrium as the effective temperature slowly
relaxes toward the bath temperature. In the other mechanism, an internal
variable directly equilibrates with the bath temperature on intermediate
timescales, without equilibrating with the effective temperature at any stage.
Both mechanisms appear to be essential for understanding the MS results.
