  We propose the entropy estimator $H_Z$, calculated from global dynamical
parameters, in an attempt to capture the degree of evolution of galaxy systems.
We assume that the observed (spatial and velocity) distributions of member
galaxies in these systems evolve over time towards states of higher dynamical
relaxation (higher entropy), becoming more random and homogeneous in virial
equilibrium. Thus, the $H_Z$-entropy should correspond to the gravitacional
assembly state of the systems. This was tested in a sample of 70 well sampled
clusters in the Local Universe whose gravitational assembly state, classified
from optical and X-ray analysis of substructures, shows clear statistical
correlation with $H_Z$. This estimator was also tested on a sample of clusters
(halos) from the IllustrisTNG simulations, obtaining results in agreement with
the observational ones.
