From modified Tsallis–Rényi entropy to a MOND-like force law, Bekenstein bound, and Landauer principle for black holes

We examine black hole thermodynamics within the framework of modified Rényi entropy and explore its implications in Modified Newtonian Dynamics (MOND), an extension of Newton's second law proposed to explain galaxy rotation curves without invoking dark matter. We conjecture that Tsallis entropy provides an exact description of Bekenstein–Hawking entropy, from which the modified Rényi entropy is derived. Using this formulation, we show that a MOND-like force law emerges naturally from entropic considerations. We also analyze the Bekenstein bound conjecture, which imposes an upper limit on the entropy of confined quantum systems, and verify its validity under the Rényi-modified framework for typical values of the deformation parameter λ. Furthermore, by invoking the Landauer principle, we obtain an expression for the mass loss due to black hole evaporation. These results suggest that modified Rényi statistics, originating from Tsallis entropy, provides a coherent and promising approach to gravitational dynamics and information-theoretic aspects of black hole physics.