Canonically invariant formulation of Langevin and Fokker-Planck Equations

TL;DR

This paper introduces a canonically invariant formulation of Langevin and Fokker-Planck equations, emphasizing the role of constants of motion and the development of conservative stochastic processes.

Contribution

It provides a new invariant framework for Langevin and Fokker-Planck equations, highlighting the importance of constants of motion in stochastic process construction.

Findings

Invariant formulation simplifies analysis of stochastic systems.

Highlights the role of conserved quantities in stochastic dynamics.

Provides a basis for constructing conservative stochastic processes.

Abstract

We present a canonically invariant form for the generalized Langevin and Fokker-Planck equations. We discuss the role of constants of motion, and the construction of conservative stochastic processes.