Thermodynamics of quantum-corrected RN-AdS black hole immersed in perfect fluid dark matter

We study the impact of spacetime quantum fluctuation on the thermodynamics of Reissner–Nordström anti-de Sitter (RN-AdS) black hole immersed in Perfect Fluid Dark Matter (PFDM). First, we add the quantum fluctuation of spacetime on the RN-AdS black hole immersed in the PFDM and write the metric, in which the quantum fluctuation effect is reflected by a parameter a. For the quantum-corrected black hole, we discover the existence of a minimum horizon radius a, also known as the remnant radius. Next, we establish the validity of the generalized Smarr relation and analyze the phase transition of the black hole. We find similarities in the phase with the van der Waals gas when the horizon radius is far larger than a, and under certain conditions, an additional unstable phase exists when the radius is near a. The critical parameters for these cases are calculated and the effects of quantum fluctuation on these critical parameters are discussed. Later, we investigate the Joule–Thomson adiabatic expansion from the thermodynamic behavior of black holes. We calculate and discuss the Joule–Thomson coefficients, and plot the inversion temperature curves and isothermal enthalpy curves.