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The temperature changes that are possible in inhomogeneous low-density astrophysical plasmas were investigated for a variety of boundary distribution functions that occur in astrophysics, with emphasis placed on the spatial changes in temperature and their correlations with those of the density caused by time-independent, but spatially varying, conservative potentials. It is proven that decelerating forces produce equilibrium temperatures that are anticorrelated with densities, provided that the boundary condition is non-Maxwellian, and the proof is extended analytically for a generalized Lorentzian distribution, showing that they obey a polytrope relation with the value of gamma between 0 and l.
J. D. Scudder (Thu,) studied this question.