Dynamic principle for ensemble control tools

Abstract: Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic principle for derivation of stochastic and deterministic thermostats. It is based on fundamental physical assumptions such that the canonical measure is invariant for the thermostat dynamics. This is a clear advantage over a range of recently proposed and widely discussed in the literature mathematical thermostat schemes. Following justification of the proposed principle we show its generality and usefulness for modeling a wide range of natural systems.