Field theoretical representation of classical statistical mechanics. I. Wave-vector space

TL;DR

This paper establishes a thermodynamic equivalence between classical many-body systems and auxiliary nonlinear fields, providing a theoretical framework that connects their Hamiltonians in wave-vector space.

Contribution

It introduces a field theoretical representation of classical statistical mechanics, linking many-body Hamiltonians to auxiliary fields in wave-vector space.

Findings

Thermodynamic equivalence between many-body systems and auxiliary fields.

Derived connection between Hamiltonians of the two systems.

Framework applicable in wave-vector space.

Abstract

Thermodynamic equivalence between classical many-body system and some auxiliary nonlinear auxiliary field is proved. Connection between Hamiltonians of the many-body system and the auxiliary field is derived.