Thermodynamic criticality and topology of the quantum-corrected RN-AdS black hole surrounded by quintessence

This paper studies the thermodynamics properties of the quantum fluctuations corrected Reissner-Nordström-Anti-de Sitter (RN-AdS) black hole surrounded by quintessence. We first investigate the basic thermodynamic quantities and the Smarr formula by treating the cosmological constant, quintessence, and quantum fluctuations parameter as thermodynamic variables in the extended phase space. The Smarr formula is given and the obtained entropy is proportional to the horizon area. Then, the thermodynamic criticality and topology are presented, and the effects of quintessence and quantum fluctuations are analyzed. The results show that, below the critical temperature, the isotherms split into stable and unstable branches. And, the quantum fluctuations can alter the global topological structure, whereas quintessence dark energy does not affect the overall topology.