Super Gaussian Self-Consistent method for systems with a two-body Hamiltonian

TL;DR

This paper introduces a novel kinetic self-consistent method based on Gaussian superposition principles to compute ensemble averages in macromolecular systems with two-body interactions, providing a tractable approach for both equilibrium and kinetic analyses.

Contribution

It presents the Super Gaussian Self-Consistent (SGSC) method, deriving a closure relation for distribution functions that simplifies the hierarchy of kinetic equations for two-body interacting systems.

Findings

Derives a functional closure relation for 3-point distribution functions.

Produces a tractable integro-differential form of the SGSC equations.

Aims to accurately model distribution functions for macromolecules with two-body interactions.

Abstract

A new kinetic self-consistent method is presented based on the proposed Gaussian Superposition Principle for computation of ensemble averaged observables of a macromolecule interacting via two-body forces. The latter leads to the derivation of a natural functional closure relation for the 3-point distribution functions (DF), thereby truncating a hierarchy of kinetic equations obtained from the original Langevin equation. The resulting Super Gaussian Self-Consistent (SGSC) equations for the 2-point distribution functions acquire a sufficiently tractable integro-differential form. The SGSC theory strives to yield realistic shapes of various distribution functions for any macromolecule with a generic Hamiltonian involving 2-body interaction potentials, both at equilibrium and during kinetics.