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 mu, 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 Tc 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 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.