  Gravity is so different from other fundamental forces that it is now
essentially treated as a non-fundamental force of entropic origin. A number of
good studies have been carried out in this direction. Quantum gravity has also
significantly improved our understanding by combining gravity well with quantum
physics. However, there are still many impediments to our understanding
especially in the limits of extreme. The effects of quantum gravity start
appearing on the scene at Planck length which is the smallest length in nature
idealized so far. While as this study incorporates a model which is valid for
potential energy corrections at small distances but we have also given a bold
try to use it confidently for the corrections at very large distances as well.
The model uses two techniques namely Boltzmann and Tsallis statistical
approaches to explore the thermodynamics within the ambit of brane world model
giving its further modified version. We have computed partition function by
using both Boltzmann and Tsallis statistical approaches and then used it to
study thermodynamics of the brane world model. We have analyzed both
analytically and graphically, the thermodynamic quantities like Helmholtz free
energy and specific heat. The thermodynamic stability of the model is also
discussed depending on the number of galaxies.
