Thermostats are often used in various condensed matter problems, e.g. when a biological molecule undergoes a transformation in a solution, a crystal surface is irradiated with energetic particles, a crack propagates in a solid upon applied stress, two surfaces slide with respect to each other, an excited local phonon dissipates its energy into a crystal bulk, and so on. In all of\ud these problems, as well as in many others, there is an energy transfer between different local parts of the entire system kept at a constant temperature. Very often, when modelling such processes using molecular dynamics simulations, thermostatting is done using strictly\ud equilibrium approaches serving to describe the NV T ensemble. In this paper we critically discuss the applicability of such approaches to non-equilibrium problems, including those mentioned above, and stress that the correct temperature control can only be achieved if the\ud method is based on the generalized Langevin equation (GLE). Specifically, we emphasize that a meaningful compromise between computational efficiency and a physically appropriate implementation of the NV T thermostat can be achieved, at least for solid state and surface\ud problems, if the so-called stochastic boundary conditions (SBC), recently derived from the GLE (Kantorovich and Rompotis 2008 Phys. Rev. B 78 094305), are used. For SBC, the Langevin thermostat is only applied to the outer part of the simulated fragment of the entire system which\ud borders the surrounding environment (not considered explicitly) serving as a heat bath. This point is illustrated by comparing the performance of the SBC and some of the equilibrium thermostats in two problems: (i) irradiation of the Si(001) surface with an energetic CaF2\ud molecule using an ab initio density functional theory based method, and (ii) the tribology of two amorphous SiO2 surfaces coated with self-assembled monolayers of methyl-terminated hydrocarbon alkoxylsilane molecules using a classical atomistic force field. We discuss the\ud differences in behaviour of these systems due to applied thermostatting, and show that in some cases a qualitatively different physical behaviour of the simulated system can be obtained if an equilibrium thermostat is used
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