Phase transition and entropy inequality of noncommutative black holes in a new extended phase space

TL;DR

This paper investigates the thermodynamics and phase transitions of noncommutative high-dimensional AdS black holes with smeared matter distributions, introducing a new extended phase space that includes a noncommutative pressure as an independent variable.

Contribution

It introduces a novel extended phase space incorporating noncommutative pressure and analyzes its effects on black hole thermodynamics and phase transitions.

Findings

Noncommutative pressure and cosmological pressure have opposite effects on phase transitions.

Black holes with Gaussian matter distribution maximize entropy for given volume.

Noncommutative effects dominate UV regime, while cosmological effects dominate IR regime.

Abstract

We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure. In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former dominates the UV regime while the latter does the IR regime, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.