Evolution Equations in Functional Derivatives of Many-Particle Systems

TL;DR

This paper formulates evolution equations for classical many-particle systems using functional derivatives, providing nonperturbative solutions and generalizations for systems with many-body interactions.

Contribution

It introduces a unified functional derivative framework for various classical hierarchies and constructs nonperturbative solution expansions, extending to many-body potentials.

Findings

Derived evolution equations in functional derivatives for classical systems

Constructed nonperturbative solution expansions for the hierarchies

Generalized results to systems with many-body interactions

Abstract

The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal distribution functions, the dual BBGKY hierarchy for marginal observables, the Liouville hierarchy for correlation functions and the nonlinear BBGKY hierarchy for the marginal correlation functions are considered. The nonperturbative solution expansions of the Cauchy problem of these hierarchies are constructed on the basis of established relations between the generating functionals of corresponding functions. The obtained results are generalized on systems of particles interacting via many-body potentials.