redefining thermodynamic potentials in 2+1 dimensional massive gravity: a minimal length approach

This work delves into the intricate relationship between quantum fluctuations and the thermodynamic properties of a (2+1)-dimensional anti-de sitter (ads) black hole. we adopt the framework of massive gravity to investigate the well-known bañados-teitelboim-zanelli (btz) black hole solution. after a concise review of the btz solution in this context, we proceed with a detailed derivation of exponentially corrected thermodynamic potentials, with careful consideration of massive gravity effects. our analysis culminates in a qualitative exploration, highlighting the dependence of these corrected potentials on the event horizon radius through a series of plots. by varying the correction parameter α, which represents the intensity of quantum fluctuations, we uncover diverse behaviors that provide insights into the complex connection between quantum phenomena and black hole thermodynamics.