Dynamic principle for ensemble control tools

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.