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tokens: et al. 2018 ). A common assumption involves the population of states, which, in the absence of knowledge to the contrary is assumed, for want of other choices , to be Maxwellian with density and temperature as parameters. This type of inversion is used to produce impressions of the temperature in plasmas far removed from the observer. A rather general argument is presented here that this mode of inverting photon information has a systematic bias by presuming the Maxwellian eVDF of the LTE when inferring the population of states involved in the line’s formation. A suggested alternative is presented based on this paper’s Steady Electron Runaway Model (SERM). Modeling astrophysical plasmas often involves solving the fluid-scale magnetohydrodynamical (MHD) equations. Within the derivation of the MHD fluid equations from the kinetic equations and their closure are further hidden assumptions of LTE (Hazeltine Walbroeck 2004 ) that are generally unwarranted on the same large scales of the modeling. These hidden assumptions also preempt consideration of non-LTE types of physics from occurring in such models (Scudder 1992 ; Meyer-Vernet et al. 1995 ). Barring improvements that do not make these small Knudsen number LTE approximations, this compromised modeling continues (Scudder 2019a ). To move beyond these (hidden) reliances on LTE requires the formulation of an alternative that challenges the likelihood that the Maxwellian eVDF is the most likely one to occur in the regions under study. To be sure, considering this possibility faces considerable resistance best redressed by studying plasmas with in situ experimental access, such as the solar wind as presented here. There finite is clearly common, and this paper argues that this parameter (or its dimensionless parallel electric field cousin) is the central index of the importance of non-Maxwellian eVDF’s that is explored in this paper. The present calculation and its comparison with solar wind measurements furthers the description of transport in plasmas with finite Knudsen number, , quantitatively defined bywhere is the local magnetic field-aligned unit vector. A fully defined Knudsen number associated with χ depends on the mean free path for scattering, , and the magnetic field-aligned scale, L , of χ . The pressure profile usually has the steepest gradient, determining the shortest transport scale L ; it thus determines the relevant for the mean free path over scale that enters as a small perturbative parameter in Chapman–Enskog closures (Chapman 1916 ; Enskog 1917 ), which are also discussed in Chapman Cowling ( 1939 ), Rossi Olbert ( 1970 ), Fitzpatrick ( 2004 ), and Zank ( 2014 ). Spitzer and Braginskii use slightly different versions of these expansions (Spitzer Harm 1953 ; Braginskii 1965 ). Between 0.3 and 5 au the observed solar wind plasma electrons possess . At 1 au (Scudder 2019b ). In all speed states of the wind “ubiquitously nonthermal” eVDF have been observed over the last 50