关键词: Reissner-Nordström qAdS black hole, restricted phase space, variable Newton constant

Abstract: We study thermodynamics of charged AdS black hole surrounded by quintessence in a new formalism which is called the restricted phase space thermodynamics. This context is based on Visser's holographic thermodynamics with a fixed anti-de Sitter radius and a variable Newton constant. The conjugate variables, central charge $C$ and the chemical potential $\mu$, are introduced as a new pair of thermodynamic variables. We find that the iso-e-charge $T$-$S$ curve becomes non-monotonic when $\hat{Q}<\hat{Q}_{\rm c}$. Correspondingly, the $F$-$T$ curve exhibits a swallow tail structure. This behavior is considered as a van der Waals-like phase transition. As the value of $\hat{b}$ related to the energy density of Kiselev's fluid becomes larger, the critical temperature $T_{\rm c}$ will decrease. Thus, the van der Waals-like phase transition will occur at lower temperature. There is always a non-quilibrium transition from a small unstable black hole to a large stable black hole state in the isocoltage $T$-$S$ process. There exist a maximum and a Hawking-Page phase transition points in the $\mu$-$C$ plane. As the value of $\hat{b}$ related to Kiselev's fluid becomes larger, the Hawking-Page phase transition will occur at lower temperature in the isovoltage $\mu$-$T$ process. For other values of the state parameter $\omega$, there also exists van der Waals-like phase transition.

Key words: Reissner-Nordström qAdS black hole, restricted phase space, variable Newton constant