Phase structures of holographic screen themodynamics

TL;DR

This paper explores the thermodynamic phase structures of holographic screens, demonstrating their phase transitions and analyzing conditions for different types of transitions in various charged spacetime scenarios.

Contribution

It establishes the connection between thermodynamics and gravity for holographic screens and classifies their phase transitions, including second order transitions, in (n+1)D RN-AdS spacetime.

Findings

Holographic screens exhibit phase transitions characterized by heat capacity discontinuities.

Second order phase transitions are confirmed via Ehrenfest equations.

Phase transition conditions depend on charge, electrostatic potential, and a parameter c.

Abstract

Holographic screens are the generalization of the event horizon of a black hole in entropic force scheme, which are defined by setting Newton potential $\phi$ constant, \textit{i. e.} $e^{2\phi}=c=$const. By demonstrating that the integrated first law of thermodynamics is equivalent to the ($r-r$) component of Einstein equations, We strengthen the correspondence between thermodynamics and gravity. We show that there are not only the first law of thermodynamics, but also kinds of phase transitions of holographic screens. These phase transitions are characterized by the discontinuity of their heat capacities. In (n+1) dimensional Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS) spacetime, we analyze three kinds of phase transitions, which are of the holographic screens with Q=0 (charge), constant $\Phi$ (electrostatic potential) and non-zero constant $Q$. In the Q=0 case, only the holographic screens with $0\le c<1$ can undergo phase transition. In the constant $\Phi$ case, the constraints become as $0\le c+16\tilde{\Gamma}^{2}\Phi^{2}<1$, where $\tilde{\Gamma}$ is a dimensional dependent parameter. By verifying the Ehrenfest equations, we show that the phase transitions in this case are all second order phase transitions. In the constant $Q$ case, there might be two, or one, or no phase transitions of holographic screens, depending on the values of $Q$ and $c$.