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

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 μ, are introduced as a new pair of thermodynamic variables. We find that the iso-e-charge T – S curve becomes non-monotonic when Q ^ Q ^ 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 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 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.