Work

The Smoluchowski–Kramers approximation for a system with arbitrary friction depending on both state and distribution

Year: 2026

Type: article

Abstract: In this paper, we study a class of stochastic differential equations modeling diffusive phenomena with state-dependent and distribution-dependent friction. In the small-mass regime, the dynamics are shown to be governed by the Smoluchowski–Kramers approximation. We obtain the limiting equation and characterize the resulting additional drift terms via solutions of associated Lyapunov and Sylvester matrix equations. Moreover, we establish the rate of convergence and extend the model to incorporate more general interaction mechanisms and noise structures.

Source: Stochastics and Dynamics

DOI: 10.1142/s0219493726500024

Authors: Xueru Liu, Qianqian Jiang, Wei Wang

Institutions: Nanjing University, Southern University of Science and Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G213363592, G3144294655