Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory - Colangeli, Matteo; Muntean, Adrian (Frontiers in Physics, 2022)
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 via the invariant manifold method, whereas the diffusion coefficient fulfills 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.