A Comprehensive Review of Geometrical Thermodynamics: From Fluctuations to Black Holes

TL;DR

This paper reviews the application of geometric methods in thermodynamics, including fluctuations, metrics, and black hole thermodynamics, highlighting recent advances and key concepts in the field.

Contribution

It provides a comprehensive overview of geometrical thermodynamics, integrating classical fluctuation theory with modern black hole thermodynamics and recent research developments.

Findings

Thermodynamic curvature reveals phase transitions.

Geometrical metrics vary across different coordinate systems.

Black hole thermodynamics can be analyzed using geometric approaches.

Abstract

This paper presents a comprehensive review of geometrical thermodynamics, which employs geometric concepts to study the thermodynamic properties of physical systems. The review covers key topics such as thermodynamic fluctuation theory, proposed thermodynamic metrics in various coordinate systems, and thermodynamic curvature. Additionally, the paper discusses the geometrical approach to black hole thermodynamics and provides an overview of recent research in this field.