Hierarchy of Fluctuation-Dissipation Theorems for the Classical One-Component Plasma

TL;DR

This paper derives higher-order fluctuation-dissipation theorems for the classical one-component plasma, linking complex structure functions to response functions, and clarifies the hierarchical structure of these relations.

Contribution

It introduces tractable cubic and quartic FDTs for the plasma, revealing the hierarchical structure and remainder contributions involving lower-order functions.

Findings

Derived cubic and quartic FDTs for plasma

Identified remainder contributions involving lower-order functions

Clarified the structure of the FDT hierarchy

Abstract

We have derived tractable cubic (p=3) and quartic (p=4) fluctuation-dissipation theorems (FDTs) for the classical one-component plasma in a form that links a single (p+1)-point dynamical structure function to a linear combination of pth-order density response functions amenable to calculation from model plasma kinetic equations. For p greater than or equal to 3, we note the emergence of "remainder" contributions comprised of clusters of lower-order dynamical structure functions which can be ultimately traded for response functions vis-a-vis the linear and quadratic FDTs. Our analysis paves the way for gaining a clear understanding of the structure of the FDT hierarchy.