Nonequilibrium entropy of a sheared gas

The nonequilibrium entropy of a dilute gas under uniform shear flow is analyzed in terms of an expansion in powers of the shear rate. To this end, the Boltzmann equation for Maxwell molecules is exactly solved to super-Burnett order, the next two orders being also partially obtained. This allows us to get the entropy through sixth order in the shear rate. Comparison with results obtained from the Bhatnagar-Gross-Krook kinetic model indicates that the latter gives a smaller entropy than the Boltzmann equation.