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

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.

arXiv comment45 pages, 7 figures, and 3 tables, an updated version