# Alternative approach to thermodynamic phase transitions

## TL;DR

This paper introduces a new theoretical method using a quasi-equation based on temperature and entropy slope to analyze thermodynamic phase transitions in black holes, offering clearer insights into their critical behavior.

## Contribution

The paper presents an alternative approach to studying black hole phase transitions that overcomes limitations of traditional methods by using a slope-based quasi-equation.

## Key findings

- Identifies phase transition points analytically.
- Determines non-physical horizon radius ranges.
- Provides a simpler, more effective analysis method.

## Abstract

One of the major open problems in theoretical physics is a consistent quantum gravity theory.Recent developments in thermodynamic phase transitions ofblack holes and their van der Waals-like behavior may provide an interesting quantum interpretation of classical gravity. Studyingdifferent methods of investigating phase transitions can extend our insight into the nature of quantumgravity. In this paper, we present an alternative theoretical approach for finding thermodynamicphase transitions in the extended phase space. Unlike the standard methods based on the usualequation of state involving temperature, our approach usesa new quasi-equation constructed fromthe slope of temperature versus entropy. This approach addresses some of the shortcomings ofthe other methods, and provides a simple and powerful way of studying the critical behavior of athermodynamical system. Among the applications of this approach, we emphasize the analyticaldemonstration of possible phase transition points, and theidentification of the non-physical rangeof horizon radii for black holes.