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

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 μ, are introduced as a new pair of thermodynamic variables. We find that the iso-e-charge T–S curve becomes non-monotonic when $\widehat{Q}<{\widehat{Q}}_{\mathrm{c}}$. 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 $\widehat{b}$ related to the energy density of Kiselev’s fluid becomes larger, the critical temperature T_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 μ–C plane. As the value of $\widehat{b}$ related to Kiselev’s fluid becomes larger, the Hawking–Page phase transition will occur at lower temperature in the isovoltage μ–T process. For other values of the state parameter ω, there also exists van der Waals-like phase transition.