The principle of maximum entropy and the distribution of mass in
  galaxies
  We do not have a final answer to the question of why galaxies choose a
particular internal mass distribution. Here we examine whether the distribution
is set by thermodynamic equilibrium (TE). Traditionally, TE is discarded for a
number of reasons including the inefficiency of two-body collisions to
thermalize the mass distribution in a Hubble time, and the fact that the mass
distribution maximizing the classical Boltzmann-Gibbs entropy is unphysical.
These arguments are questionable. In particular, when the Tsallis entropy that
describes self-gravitating systems is used to define TE, the mass distributions
that result (i.e., the polytropes) are physically sensible. This work spells
out this and other arguments for TE, and presents the polytropes and their
properties. It puts forward empirical evidence for the mass distribution
observed in galaxies to be consistent with polytropes. It compares polytropes
with Sersic functions and it shows how the DM halos resulting from cosmological
numerical simulations become polytropes when efficient collisions are allowed.
It also discusses pathways to thermalization bypassing two-body collisions. It
finally outlines future developments including deciphering whether or not DM
particles collide efficiently.
