Notes on configurational thermostat schemes.

The simulation of rheological properties of molecular fluids requires realistic temperature control correctly taking into account the streaming velocity of the fluid. This has become feasible following the introduction of thermostatting techniques defining temperature using only configurational variables. Configurational approaches are also important in many other contexts, for example, in systems subject to an external pressure constraint and in understanding conformational dynamics of biomolecules. In a series of papers, Braga and Travis BT proposed a Nosé–Hoover type thermostat based on a configurational definition of temperature in short BT thermostat , removing difficulties associated with the earlier Delhomelle–Evans approach, which, for example, does not preserve the canonical distribution in the equilibrium case. Recently, the BT thermostat has had further attention, development, and application in the literature. In the principal paper, the authors considered the configurational thermostat scheme proposed in Refs. 12 and 13 Samoletov-Dettmann-Chaplain, in short, SDC scheme as a starting point and then presented their own configurational temperature thermostat as a further development of the SDC scheme. Correct action of both BT and SDC thermostats has been confirmed by a variety of numerical simulations in these works. In this note, we link together two above-mentioned contributions in the development of configurational thermostats and thus accomplish two goals. First, we show that the configurational temperature BT thermostat is a particular case of the SDC scheme. Second, we demonstrate how this particular case benefits from the general method in a variety of aspects including the physical context, a stochastic counterpart thermostat to the authors’ knowledge, this has not previously appeared in the literature , and ergodicity issues.