Fractional-order phase transition of charged AdS black holes

Abstract

Employing the fractional derivatives, we construct a more elaborate classification of phase transitions compared to the original Ehrenfest classification. In this way, a thermodynamic system can even undergo a fractional-order phase transition. We use this method to restudy the charged AdS black hole and Van der Waals fluids and find that at the critical point they both have a 4/3-order phase transition, but not the previously recognized second-order one.

Fingerprinting the Fractional Order Phase Transitions in AdS Black Holes

“…When β > 4/3, the ß-order fractional derivatives of the Gibbs free energy diverge. Hence, as for 4D RN-AdS black holes [1], the FPT order of the RN-AdS black hole surrounded by quintessence is β 4/3. This is clearly illustrated by the left panel of Figure 1 where the fractional derivative D β t g is plotted as a function of the reduced temperature t for several values of β: β 9/6, 9/8, and 4/3 near the critical point.…”

“…The generalized Ehrenfest classification holds for all thermodynamic systems having phase structures, including AdS black holes with analogous behavior to Van der Waals gases. Indeed, a first study recently performed by Ma [1] showed that RN-AdS black holes can undergo 4/3 order FPT. In this paper, we aim to explore further this issue and see whether this fractional order holds for any AdS black hole solution, as in VdW systems.…”

Edge fluctuations and third-order phase transition in harmonically confined long-range systems

“…One naturally wonders how this fluctuation of y max compares with the mean of the separation between the scaled positions of the rightmost and the second rightmost particles denoted as ∆ edge . The N dependence of this average separation at the edge § Alternatively, the Ehrenfest classification [62][63][64] can be generalised by extending the notion of normal derivatives to fractional derivatives [65][66][67] can be obtained using the "Lifshitz argument", which is frequently used in extreme value statistics [14,17]. According to this argument…”

Fingerprinting the fractional order phase transitions in AdS black holes

“…

In this paper, we have extended and deepened the study on fractional order phase transition (FPT) of a charged AdS black hole performed in [1]. We have carried out a detailed analysis of FPT for three AdS black hole prototypes: black hole surrounded by quintessence background, 5D Gauss-Bonnet, and lastly Kerr black holes.

…”

“…The generalized Ehrenfest classification holds for all thermodynamic systems having phase structures, including AdS black holes with analogous behaviour to Van der Waals gases. Indeed, a first study recently performed by Ma [1] showed that RN-AdS black holes can undergo 4/3 order FPT. In this paper, we aim to explore further this issue and see whether this fractionnal order holds for any AdS black hole solution, as in VdW systems.…”