Thermodynamics of charged Bardeen-AdS black hole with perfect fluid dark matter and cloud of strings

We study the extended phase space thermodynamics of a charged Bardeen-Anti-de Sitter (AdS) black hole (BH) surrounded by perfect fluid dark matter (PFDM) and a cloud of strings (CS). The metric function carries five parameters: magnetic charge q , electric charge Q , CS parameter a , PFDM parameter β , and cosmological constant Λ. The CS enlarges the event horizon while PFDM reduces it. The entropy is fixed by the Bekenstein-Hawking area law S = A / 4 , in agreement with Wald’s Noether-charge prescription, and the thermodynamic analysis is carried out within the reduced thermodynamic phase space (RTPS) framework of Ma–Li–Shi and Ma–He–Wang–Li, in which all physical quantities are first defined in the full phase space of the underlying singular “mother” BH and are then projected onto the regular sector via the Bardeen regularity constraint. Thermal fluctuations yield positive corrections (Δ S > 0) with relative magnitude below 18% for large BHs. The Joule-Thomson analysis shows that the Bardeen core and CS decrease the inversion temperature, contracting the cooling region. The critical ratio ρ c = P c r c / T c ≈ 0.19 deviates from the Reissner-Nordström-AdS universal value 3/8, while van der Waals-like phase transitions persist with mean-field exponents. For a rectangular heat engine cycle, the efficiency reaches 67% of the Carnot bound. Within the parameter window we sample, these results identify quantitative thermodynamic shifts produced by exotic matter fields surrounding regular AdS BHs, with the inherited and the new pieces separated explicitly in the body of the text.