AUTHOR=Colangeli Matteo , Muntean Adrian TITLE=Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory JOURNAL=Frontiers in Physics VOLUME=10 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.903030 DOI=10.3389/fphy.2022.903030 ISSN=2296-424X 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.