The content of my book proves beyond doubt that isothermal conditions are not the state of thermodynamic equilibrium in a gravitational field or any force field. (judithcurry.com)
Gerhard Gerlich an expert in thermodynamics and the modeling of thermodynamic systems said it all in this paper: (notrickszone.com)
When a gas is in LTE then the absorption and emission is isotropic, but when Milne came up with the idea of LTE he wrote «This permits us to see in a general way why the state of local thermodynamic equilibrium in the interior of a star breaks down as we approach the surface.» (realclimate.org)