  Violent relaxation has been proposed half a century ago to bear
responsibility for non-collisional dynamics and formation of gravitationally
bound systems of extended celestial objects (agglomeration of stars, galaxies,
clusters of galaxies) when reaching an approximate equilibrium state which can
be described thermodynamically. The Lynden-Bell equilibrium distribution of
such systems, resulting from a spatial exclusion principle, had been shown to
be an analog to the Fermi distribution of states in solid state physics. Real
extended objects like galaxies do not completely exclude each other, however.
Permitting for partial exclusion leads to a modification of the equilibrium
distribution. Here we show that this case can be treated in analogy to a
hypothetical incomplete population of Fermi states. An incomplete-exclusion
equilibrium distribution is obtained which enters the violent relaxation
theory.
