Thermodynamics of ideal gases under shear: a maximum-entropy approach

The maximum-entropy formalism is used here as a basis of a thermodynamic description of ideal gases under shear. We have obtained expressions for the entropy and the equations of state in nonequilibrium steady states characterized by a given shear viscous pressure and have identified in physical terms the Lagrange multiplier conjugated to the viscous 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 viscosity at high shear rates and also show how previous results of nonequilibrium molecular dynamics could be compatible with our thermodynamic analysis.