  The Kovacs or crossover effect is one of the peculiar behaviours exhibited by
glasses and other complex, slowly relaxing systems. Roughly it consists in the
non-monotonic relaxation to its equilibrium value of a macroscopic property of
a system evolving at constant temperature, when starting from a non-equilibrium
state. Here, this effect is investigated for general systems whose dynamics is
described by a master equation. To carry out a detailed analysis, the limit of
small perturbations in which linear response theory applies is considered. It
is shown that, under very general conditions, the observed experimental
features of the Kovacs effect are recovered. The results are particularized for
a very simple model, a two-level system with dynamical disorder. An explicit
analytical expression for its non-monotonic relaxation function is obtained,
showing a resonant-like behaviour when the dependence on the temperature is
investigated.
