Galilean-invariant Nosé-Hoover-type thermostats

A new pairwise Nosé-Hoover type thermostat for molecular dynamics (MD) simulations which is similar in construction to the pair-velocity thermostat of Allen and Schmid, [Mol. Simul. 33, 21 (2007)] (AS) but is based on the configurational thermostat is proposed and tested. Both thermostats generate the canonical velocity distribution, are Galilean invariant, and conserve linear and angular momentum. The unique feature of the pairwise thermostats is an unconditional conservation of the total angular momentum, which is important for thermalizing isolated systems and those nonequilibrium bulk systems manifesting local rotating currents. These thermostats were benchmarked against the corresponding Nosé-Hoover (NH) and Braga-Travis prescriptions, being based on the kinetic and configurational definitions of temperature, respectively. Some differences between the shear-rate-dependent shear viscosity from Sllod nonequilibrium MD are observed at high shear rates using the different thermostats. The thermostats based on the configurational temperature produced very similar monotically decaying shear viscosity (shear thinning) with increasing shear rate, while the NH method showed discontinuous shear thinning into a string phase, and the AS method produced a continuous increase of viscosity (shear thickening), after a shear thinning region at lower shear rates. Both pairwise additive thermostats are neither purely kinetic nor configurational in definition, and possible directions for further improvement in certain aspects are discussed.