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

Incomplete-exclusion Statistical Mechanics in Non-collisional Violent Relaxation of Celestial Objects