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Abstract

The research paper investigates the thermodynamic behavior of a black hole in a cloud of strings (CoS) and perfect fluid dark matter (PFDM), incorporating a minor correction to the Anti de Sitter (AdS) length scale. The study reveals that while the entropy remains unaffected by the AdS length correction, other thermodynamic quantities such as enthalpy, free energy, pressure, internal energy, Gibbs free energy, and heat capacity exhibit significant modifications. Positive corrections to the AdS length generally enhance these quantities, leading to faster growth or slower decay with increasing black hole size, while negative corrections often produce the opposite effect, sometimes resulting in divergent or negative values. These findings highlight the sensitivity of black hole thermodynamics to geometric corrections and exotic matter fields, providing deeper information about the interplay between such modifications and thermodynamic stability. These results underscore the importance of considering minor corrections in theoretical models to better understand black hole behavior in the presence of dark matter and string-like matter distributions.