The recently developed concept of "entropic defect" is important for
understanding the foundations of thermodynamics in space plasma physics, and
more generally, for systems with physical correlations among their particles.
Using this concept, this paper derives the basic formulation of the
distribution function of velocities (or kinetic energies) in space plasma
particle populations. Earlier analyses have shown how the formulation of kappa
distributions is interwoven with the presence of correlations among the
particles' velocities. This paper shows, for the first time, that the reverse
is true: the thermodynamics of particles' physical correlations are consistent
only with the existence of kappa distributions.Comment: 19 pages, 3 figure