On the Thermodynamic Geometry of Hot QCD

TL;DR

This paper explores the thermodynamic geometry of hot QCD, demonstrating a well-defined geometric structure without singularities and linking it to quark susceptibilities near the QCD transition.

Contribution

It introduces a systematic geometric framework for hot QCD thermodynamics, including thermal fluctuations, and connects this geometry to correlation measures.

Findings

Thermodynamic geometry of hot QCD is well-defined and non-singular.

The geometric approach correlates with quark number susceptibilities.

Analysis includes both 2- and 3-flavor QCD near transition temperature.

Abstract

We study the nature of the covariant thermodynamic geometry arising from the free energy of hot QCD. We systematically analyze the underlying equilibrium thermodynamic configurations of the free energy of 2- and 3-flavor hot QCD with or without including thermal fluctuations in the neighborhood of the QCD transition temperature. We show that there exists a well-defined thermodynamic geometric notion for QCD thermodynamics. The geometry thus obtained has no singularity as an intrinsic Riemannian manifold. We further show that there is a close connection of this geometric approach with the existing studies of correlations and quark number susceptibilities in hot QCD.