Simplified Derivation of the Non-Equilibrium Probability Distribution

TL;DR

This paper presents a clear and straightforward derivation of the exact probability distribution for classical non-equilibrium systems, along with the associated stochastic, dissipative equations of motion.

Contribution

It offers a simplified and transparent derivation of non-equilibrium probability distributions and equations of motion, enhancing understanding of classical non-equilibrium statistical mechanics.

Findings

Derivation of the exact non-equilibrium probability distribution

Formulation of stochastic, dissipative equations of motion

Simplified approach improves conceptual clarity

Abstract

A simple and transparent derivation of the formally exact probability distribution for classical non-equilibrium systems is given. The corresponding stochastic, dissipative equations of motion are also derived.