The maximum-entropy formalism is used here as a basis of a thermodynam
ic description of ideal gases under shear. We have obtained expression
s for the entropy and the equations of state in nonequilibrium steady
states characterized by a given shear viscous pressure and have identi
fied in physical terms the Lagrange multiplier conjugated to the visco
us pressure. Our results for those thermodynamic quantities generalize
previous expressions which were limited to second order in the shear
viscous pressure. These results show a reduction of the shear viscosit
y at high shear rates and also show how previous results of nonequilib
rium molecular dynamics could be compatible with our thermodynamic ana
lysis.