  The Kovacs effect is a remarkable feature of the ageing dynamics of glass
forming liquids near the glass transition temperature. It consists in a
non-monotonous evolution of the volume/enthalpy after a succession of two
abrupt temperature changes: first from a high initial temperature $T_i$ to a
much lower annealing temperature $T_a$ followed by a smaller second jump back
to a slightly higher final temperature $T_f$. The second change is performed
when the instantaneous value of the volume/enthalpy coincides with the
equilibrium one at the final temperature. While this protocol might be expected
to yield equilibrium dynamics right after the second temperature change, one
observes the so-called Kovacs hump in glassy systems. In this paper we apply
such thermal protocol to the Distinguishable Particles Lattice Model (DPLM) for
a wide range of fragility of the system. We study the Kovacs hump based on
energy relaxation and all main experimental features are captured. Results are
compared to general predictions based on a master equation approach in the
linear response limit. We trace the origin of the Kovacs hump to the
non-equilibrium nature of the probability distribution of particle interaction
energies after the annealing and find that its difference with respect to the
final equilibrium distribution is non-vanishing with two isolated zeros. This
allows Kovacs' condition of equilibrium total energy to be met
out-of-equilibrium, thus representing the memory content of the system.
Furthermore, the hump is taller and occurs at a larger overlap with the system
initial configuration for more fragile systems. The dynamics of a structural
temperature for the mobile regions strongly depends on the glass fragility
while for the immobile ones only a weak dependence is found.
