Universal Form of Stochastic Evolution for Slow Variables in Equilibrium Systems

Abstract

Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that obtained by Green. An equation with a nonlinear friction term for Brownian motion turns out to be an example of the general results. A key method in our derivation is to use different discretization schemes in a path integral formulation and the corresponding Langevin equation, which also leads to a consistent understanding of apparently different expressions for the path integral in previous studies.

arXiv comment17 pages

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• Stochastic order parameter dynamics for phase coexistence in heat conduction
• Coarse-Graining of Microscopic Dynamics into Mesoscopic Transient Potential Model
• Time-Slicing Path-integral in Curved Space
• Supersymmetries in non-equilibrium Langevin dynamics
• Dissipation in Langevin Equation and Construction of Mobility Tensor from Dissipative Heat Flow
• Coupling an elastic string to an active bath: the emergence of inverse damping
• Imitating non-equilibrium steady states using time-varying equilibrium force in many-body diffusive systems
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Restoring the second law to classical-quantum dynamics
• Lagrangian dynamics in inhomogeneous and thermal environments, An application of the Onsager-Machlup theory I