The Quasi-localized Einstein and M{\o}ller Energy Complex as Thermodynamic Potentials

TL;DR

This paper explores the Einstein and Møller energy complexes in PG coordinates, proposing their roles as thermodynamic potentials and analyzing their differences through a Legendre transformation analogy.

Contribution

It introduces a novel thermodynamic interpretation of Einstein and Møller energy complexes as internal and Helmholtz energies.

Findings

Energy difference resembles Legendre transformation

Energy complexes act as thermodynamic potentials

Provides new perspective on gravitational energy localization

Abstract

In this article, I obtain the Einstein and M{\o}ller energy complex in PG coordinates. According to the difference of energy within radius $r$ between Einstein and M{\o}ller prescription, I could present the difference of energy within radius $r$ like the fomula of Legendre transformation and propose that the M{\o}ller and Einstein energy complex play the role of internal energy and Helmholtz energy in thermodynamics.