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Progress in our understanding of auroral currents and auroral electron acceleration has for decades been hampered by an apparent incompatibility between kinetic and fluid models of the physics involved. A well established kinetic model predicts that steady upward field-aligned currents should be linearly related to the potential drop along the field line, but collisionless fluid models that reproduce this linear current-voltage relation have not been found. Using temperatures calculated from the kinetic model in the presence of an upward auroral current, we construct here approximants for the parallel and perpendicular temperatures. Although our model is rather simplified, we find that the fluid equations predict a realistic large-scale parallel electric field and a linear current-voltage relation when these approximants are employed as nonlocal equations of state. This suggests that the concepts we introduce can be applied to the development of accurate equations of state for fluid simulations of auroral flux tubes.<br><br><b>Key words.</b> Magnetospheric physics (auroral phenomena; magnetosphere-ionosphere interactions) – Space plasma physics (kinetic and MHD theory)