Fractional phase transitions of RN-AdS black hole at Davies points

TL;DR

This paper investigates the fractional order phase transitions of RN-AdS black holes at Davies points using a generalized Ehrenfest classification, revealing different transition orders and offering new insights into black hole thermodynamics.

Contribution

It introduces a fractional derivative-based classification to distinguish phase transition orders at Davies points of RN-AdS black holes, refining the traditional second-order framework.

Findings

Phase transitions at Davies points have fractional orders: 3/2 and 4/3.

The generalized Ehrenfest classification differentiates transition types.

Provides a finer understanding of black hole thermodynamic phase transitions.

Abstract

We perform a study of phase transitions of RN-AdS black hole at its Davies points according to a generalized Ehrenfest classification of phase transition established on the basis of fractional derivatives. Davies points label the positions where heat capacity diverges. According to the usual Ehrenfest classification, second-order phase transitions occur there. For RN-AdS black hole, the Davies points can be classified into two types. The first type corresponds to the extreme values of temperature and the second type corresponds to the infection point(namely the critical point) of temperature. Employing the generalized Ehrenfest classification, we find that the orders of phase transition at the two types of Davies points are different. It is $3/2$-order for the first type and $4/3$-order for the second type. Thus this finer-grained classification can discriminate phase transitions that are supposed to be in the same category, which may provide some new insights toward a better understanding of black hole thermodynamics.