# Dynamic principle for ensemble control tools

## TL;DR

This paper introduces a new dynamic principle for deriving thermostats used in statistical mechanics, ensuring the canonical measure remains invariant, which enhances modeling of natural systems.

## Contribution

It proposes a fundamental dynamic principle for deriving both stochastic and deterministic thermostats, improving their physical consistency and applicability.

## Key findings

- The principle guarantees invariance of the canonical measure.
- It is applicable to a wide range of natural systems.
- The approach offers a unified framework for thermostat design.

## 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.