  Whereas the original Boltzmann's $H$-theorem applies to elastic collisions,
its rigorous generalization to the inelastic case is still lacking.
Nonetheless, it has been conjectured in the literature that the relative
entropy of the velocity distribution function with respect to the homogeneous
cooling state (HCS) represents an adequate nonequilibrium entropy-like
functional for an isolated freely cooling granular gas. In this work, we
present molecular dynamics results reinforcing this conjecture and rejecting
the choice of the Maxwellian over the HCS as a reference distribution. These
results are qualitatively predicted by a simplified theoretical toy model.
Additionally, a Maxwell-demon-like velocity-inversion simulation experiment
highlights the microscopic irreversibility of the granular gas dynamics,
monitored by the relative entropy, where a short ``anti-kinetic'' transient
regime appears for nearly elastic collisions only.
