  We investigate kinetic entropy-based measures of the non-Maxwellianity of
distribution functions in plasmas, i.e., entropy-based measures of the
departure of a local distribution function from an associated Maxwellian
distribution function with the same density, bulk flow, and temperature as the
local distribution. First, we consider a form previously employed by Kaufmann
and Paterson [{\it J.~Geophys.~Res.,} {\bf 114}, A00D04 (2009)], assessing its
properties and deriving equivalent forms. To provide a quantitative
understanding of it, we derive analytical expressions for three common
non-Maxwellian plasma distribution functions. We show that there are
undesirable features of this non-Maxwellianity measure including that it can
diverge in various physical limits and elucidate the reason for the divergence.
We then introduce a new kinetic entropy-based non-Maxwellianity measure based
on the velocity-space kinetic entropy density, which has a meaningful physical
interpretation and does not diverge. We use collisionless particle-in-cell
simulations of two-dimensional anti-parallel magnetic reconnection to assess
the kinetic entropy-based non-Maxwellianity measures. We show that regions of
non-zero non-Maxwellianity are linked to kinetic processes occurring during
magnetic reconnection. We also show the simulated non-Maxwellianity agrees
reasonably well with predictions for distributions resembling those calculated
analytically. These results can be important for applications, as
non-Maxwellianity can be used to identify regions of kinetic-scale physics or
increased dissipation in plasmas.
