Entropy Production in Collisionless Systems. I. Large Phase-Space
  Occupation Numbers
  Certain thermal non-equilibrium situations, outside of the astrophysical
realm, suggest that entropy production extrema, instead of entropy extrema, are
related to stationary states. In an effort to better understand the evolution
of collisionless self-gravitating systems, we investigate the role of entropy
production and develop expressions for the entropy production rate in two
particular statistical families that describe self-gravitating systems. From
these entropy production descriptions, we derive the requirements for
extremizing the entropy production rate in terms of specific forms for the
relaxation function in the Boltzmann equation. We discuss some implications of
these relaxation functions and point to future work that will further test this
novel thermodynamic viewpoint of collisionless relaxation.
