Covariant Formulation of Non-linear Langevin Theory with Multiplicative Gaussian White Noises

Abstract

The multi-dimensional non-linear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to non-linear transform of variables. The formalism involves no metric or affine connection, works for systems with or without detailed balance, and is substantially simpler than previous theories. Its relation with deterministic theory is clarified. The unitary limit and Hermitian limit of the theory are examined. Some implications on the choices of stochastic calculus are also discussed.

12 pages, no figures

References in corpus (4)

• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Universal Form of Stochastic Evolution for Slow Variables in Equilibrium Systems
• Langevin dynamics for vector variables driven by multiplicative white noise: a functional formalism