  We observe a significant steady-state deviation from the generalized
equipartition theorem, one of the pivotal results of classical statistical
mechanics, in a system of confined, laser cooled atoms. We quantify this
deviation, measure its dynamics and show that its steady state value quantifies
the departure of non-thermal states from thermal equilibrium even for
anharmonic confinement. In particular, we find that deviations from
equipartition grow as the system dynamics becomes more anomalous. We present
numerical simulations that validate the experimental data and reveal an
inhomogeneous distribution of the kinetic energy through the system, supported
by an analytical analysis of the phase space.m, supported by an analytical
analysis of the phase space.
