A geometric description of blackbody-like systems in thermodynamic equilibrium

TL;DR

This paper employs geometric formalisms to analyze electromagnetic radiation-like systems in thermodynamic equilibrium, classifying their properties and confirming the non-interaction hypothesis through curvature scalar evaluation.

Contribution

It introduces a geometric framework to study blackbody-like systems, classifies systems based on metric determinant behavior, and confirms the non-interaction hypothesis via curvature scalar analysis.

Findings

Vanishing metric determinant classifies non-generalizable systems.

Thermodynamic curvature scalar $ ext{R}=0$ confirms non-interacting systems.

Geometric formalism provides insights into thermodynamic properties of radiation-like systems.

Abstract

Riemannian and contact geometry formalisms are used to study the fundamental equation of electromagnetic radiation-like systems, obeying a Stefan-Boltzmann's-like law. The vanishing of metric determinant is used for classifying what kind of systems can not represent a possible generalization of blackbody-like systems. In addition, thermodynamic curvature scalar $\mathcal{R}$ is evaluated for a thermodynamic metric, giving $\mathcal{R}=0$, which validates the non-interaction hypothesis stating that the scalar curvature vanishes for non-interacting systems.