Hamza TariqSP22-RMT-001Dr. Abdul JawadLHR TP 87102026-03-132023-03-13https://repository.cuilahore.edu.pk/handle/123456789/2809In this thesis, we explore the thermodynamic characteristics of a Bardeen black hole that interacts with a string cloud and is minimally connected to nonlinear electrodynamics. We present a entropy function with five parame ters, demonstrating its singularity-free behavior throughout the entire cos mic evolution of the universe. Moreover, this function serves to extend the Tsallis, R´enyi, and Sharma-Mittal entropies for appropriate parameter limit conditions.For instance the Tsallis entropy is expressed as ST = S δ , where δ represents the Tsallis exponent and S denotes the Bekenstein-Hawking entropy. This formula is particularly applicable to systems with long-range interactions where the Boltzmann-Gibbs entropy is not suitable. It’s evident that when δ = 1, the Tsallis entropy converges to the BekensteinHawking limit, but for values of δ other than 1, it does not exhibit additivity. On the contrary, the R´enyi entropy it converges to the Bekenstein-Hawking limit as a approaches zero. While the Tsallis and R´enyi entropies might be combined to generate the Sharma-Mittal entropy, the R´enyi entropy was first offered as a way to assess information content. We analyze a variety of parameters, including mass, temperature, pressure, and Gibbs free en ergy, using the Tsallis, R´enyi, and Sharma-Mittal entropies. In our study, we derive stable behavior and find physical solutions by taking particular values for the parameters a and q.enDepartment of MathematicsMathematicsSP22thermodynamiccharacteristicsnonlinear electrodynamicsThesis