Thermodynamics of charged AdS black hole surrounded by quintessence in restricted phase space

Abstract

In this paper, we study the thermodynamics of charged AdS black hole surrounded by quintessence in a new formalism which is called the restricted phase space thermodynamics(RPST). This context is based on the 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 have found that the iso-e-charge $T-S$ curve becomes non-monotonic when $\hat{Q}＜\hat{Q}_{c}$. And 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 gets larger, the critical temperature $T_c$ will decrease. So the Van der Waals-like phase transition will occure 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. And there contains a maximuma and a Hawking-Page phase transition point in the $\mu-C$ plane. As the value of $\hat{b}$ related to Kiselev's fluid gets larger, the Hawking-Page phase transition will occur at the lower temperature in the isovoltage $\mu-T$ process. For the other values of the state parameter $\omega$, there also exists Van der Waals-like phase transition.