Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory
arXiv:2109.10745 · doi:10.3389/fphy.2022.903030
Abstract
We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the Dynamic Invariance principle, whereas the diffusion coefficient fulfils the Fluctuation-Dissipation theorem. Explicit calculations are carried out in the case of a harmonically bound particle. A quantitative pointwise representation of the reduction error is also provided and connections to both the Maximum Entropy method and the linear response theory are highlighted. Our study paves the way to the development of reduction procedures applicable to a wider class of diffusion processes.
References in corpus (6)
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Normal form transforms separate slow and fast modes in stochastic dynamical systems
- Exact linear hydrodynamics from the Boltzmann equation
- From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations
- Hyperbolicity of exact hydrodynamics for three-dimensional linearized Grad's equations
- Response Theory and Phase Transitions for the Thermodynamic Limit of Interacting Identical Systems