A kinetic discussion is presented of the temperature changes possible in inhomogeneous, low-density plasmas for a variety of boundary distribution functions that occur in astrophysics. Emphasis is placed on the spatial changes in temperature and their correlations with those of the density caused by time-independent, but spatially varying, conservative potentials; examples from in situ space plasma measurements where these effects have been documented are organized by this approach. Where equivalent polytropes are determined, they are shown to have exponents gamma greater than, equal to, and less than unity. A graphical proof is provided that decelerating forces produce equilibrium temperatures that are anticorrelated with densities provided that the boundary condition is non-Maxwellian. This proof is extended analytically for a generalized Lorentzian distribution to show that they obey a polytrope relation with 0 < gamma < 1. Five factors influence the interactions of a gas with these potentials: (1) the boundary Mach number of the flow, (2) the proximity of the initial velocity distribution to a convected Maxwellian, (3) the relative size of the convection energy and the energy change associated with the potential, (4) the repulsive or attractive nature of the potential, and (5) the collisionality and degree of ionization of the medium. In the presence of spatial variations of the potential energy, general rules for the accompanying temperature profiles are developed. This temperature, the root mean square of the distribution of particle speeds, has a spatial variation for all circumstances except decelerating forces acting on Maxwellian distribution at rest. These changes are observed in numerous in situ contexts of space plasmas as well as in laboratory apparatus with charged particle beams. Considering the generality of the argument and the ubiquity of nonthermal phase-space distributions wherever in situ space plasma measurements are made, and the inability of residual Coulomb scattering in a fully ionized, inhomogeneous plasma to suppress these effects, these considerations raise new possibilities for the interpretation of remote astrophysical observations with conclusions potentially different from those permitted by classical thermodynamical arguments. These new possibilities occur when the traditional plasma fluid closure/truncation schemes are relaxed to address the consequences of nonnegligible suprathermal populations that are routinely sampled by spacecraft.
