# Geometrothermodynamics as a singular conformal thermodynamic geometry

## TL;DR

This paper introduces a new formalism for thermodynamic geometry that is conformally related to geometrothermodynamics (GTD), effectively excluding unphysical points through a singular conformal transformation.

## Contribution

It redefines thermodynamic geometry using Jacobian coordinate transformations and demonstrates that this new formalism avoids unphysical points inherent in GTD.

## Key findings

- New formalism is conformally related to GTD
- Excludes unphysical points without constraints
- Provides a clearer thermodynamic geometric framework

## Abstract

In this letter, we first redefine our formalism of the thermodynamic geometry introduced in [1,2] by changing coordinates of the thermodynamic space by means of Jacobian matrices. We then show that the geometrothermodynamics (GTD) is conformally related to this new formalism of the thermodynamic geometry. This conformal transformation is singular at unphysical points were generated in GTD metric. Therefore, working with our metric neatly excludes all unphysical points without imposing any constraints.