  Cosmological N-body simulations represent an excellent tool to study the
formation and evolution of dark matter (DM) halos and the mechanisms that have
originated the universal profile at the largest mass scales in the Universe. In
particular, the combination of the velocity dispersion $\sigma_\mathrm{v}$ with
the density $\rho$ can be used to define the pseudo-entropy
$S(r)=\sigma_\mathrm{v}^2/\rho^{\,2/3}$, whose profile is well-described by a
simple power-law $S\propto\,r^{\,\alpha}$. We analyze a set of cosmological
hydrodynamical re-simulations of massive galaxy clusters and study the
pseudo-entropy profiles as traced by different collisionless components in
simulated galaxy clusters: DM, stars, and substructures. We analyze four sets
of simulations, exploring different resolution and physics (N-body and full
hydrodynamical simulations) to investigate convergence and the impact of
baryons. We find that baryons significantly affect the inner region of
pseudo-entropy profiles as traced by substructures, while DM particles profiles
are characterized by an almost universal behavior, thus suggesting that the
level of pseudo-entropy could represent a potential low-scatter mass-proxy. We
compare observed and simulated pseudo-entropy profiles and find good agreement
in both normalization and slope. We demonstrate, however, that the method used
to derive observed pseudo-entropy profiles could introduce biases and
underestimate the impact of mergers. Finally, we investigate the pseudo-entropy
traced by the stars focusing our interest in the dynamical distinction between
intracluster light (ICL) and the stars bound to the brightest cluster galaxy
(BCG): the combination of these two pseudo-entropy profiles is well-described
by a single power-law out to almost the entire cluster virial radius.
