Temperature and temperature control in nonequilibrium-molecular-dynamics simulations of the shear flow of dense liquids

Methodological problems of the temperature control (thermostat) in nonequilibrium-molecular-dynamics simulations of dense liquids undergoing a stationary planar shear flow are addressed. They arise in connection with a transition into a shear-induced ordered state at high shear rates which goes along with inhomogeneities of the fields of density, temperature, and velocity gradient (shear rate) on the length scale of a particle diameter. We demonstrate that a meaningful local description of the thermodynamic fields can be achieved by a smoothing procedure. In particular, the local temperature is related to the width of a local Maxwellian velocity-distribution function. These results are employed for a formulation of a so-called profile-unbiased thermostat which fulfills the criterion of the local-equilibrium hypothesis.