Thermodynamic integration for the determination of nonequilibrium entropy

Planar shear flow described by the SLLOD algorithm is a well-defined nonequilibrium steady state system with strong nonlinearity. Equipped with a numerical feedback thermostat it produces stable averages and fluctuations. We assume that moving infinitely slowly and isoenergetically along nonequilibrium states the excess rate at which heat is removed from the system can determine the work needed to move the system from equilibrium to steady states far from equilibrium. The excess heat rate is measured relative to the average heat rate of the corresponding steady state. As the best approximation, we use the configurational temperature to obtain entropy from the excess work in the typical shear rate range of simulations.