Cluster expansions of particle system state with topological nearest-neighbor interaction
Mathematical Physics
2025-12-30 v1 Statistical Mechanics
Analysis of PDEs
Dynamical Systems
math.MP
Abstract
The article presents the concept of a cumulant representation for distribution functions describing the states of many-particle systems with topological nearest-neighbor interaction. A solution to the Cauchy problem for the hierarchy of nonlinear evolution equations for the cumulants of distribution functions of such systems is constructed. The connection between the constructed solution and the series expansion structure for a solution to the Cauchy problem of the BBGKY hierarchy has been established. Furthermore, the expansion structure for a solution to the Cauchy problem of the hierarchy of evolution equations for reduced observables of topologically interacting particles is established.
Keywords
Cite
@article{arxiv.2503.08412,
title = {Cluster expansions of particle system state with topological nearest-neighbor interaction},
author = {V. I. Gerasimenko and I. V. Gapyak},
journal= {arXiv preprint arXiv:2503.08412},
year = {2025}
}
Comments
21 pages