  A common approach to assess the nature of energy conversion in a classical
fluid or plasma is to compare power densities of the various possible energy
conversion mechanisms. A forefront research area is quantifying energy
conversion for systems that are not in local thermodynamic equilibrium (LTE),
as is common in a number of fluid and plasma systems. Here, we introduce the
``higher-order non-equilibrium term'' (HORNET) effective power density that
quantifies the rate of change of departure of a phase space density from LTE.
It has dimensions of power density, which allows for quantitative comparisons
with standard power densities. We employ particle-in-cell simulations to
calculate HORNET during two processes, namely magnetic reconnection and
decaying kinetic turbulence in collisionless magnetized plasmas, that
inherently produce non-LTE effects. We investigate the spatial variation of
HORNET and the time evolution of its spatial average. By comparing HORNET with
power densities describing changes to the internal energy (pressure dilatation,
$\rm{Pi-D}$, and divergence of the vector heat flux density), we find that
HORNET can be a significant fraction of these other measures (8\% and 35\% for
electrons and ions, respectively, for reconnection; up to 67\% for both
electrons and ions for turbulence), meaning evolution of the system towards or
away from LTE can be dynamically important. Applications to numerous plasma
phenomena are discussed.
