Corrections to the thermodynamic quantities of Bose system by the generalized uncertainty principle

This paper investigated the Bose system in a spherical shell close to the black hole horizon. Several thermodynamic quantities of the Bose system are derived, which are different from those in the flat spacetime, by introducing the generalized uncertainty principle (GUP) into the grand partition function of statistical mechanics. The internal energy and the pressure of the Bose system appear to have a correction term of $T^6$, while the entropy has a $T^5$ correction term where both the coefficients are functions of the spacetime component $g_{00}$ and the brick-wall model parameter $\epsilon$. Taking the Schwarzschild black hole as an example, the physical quantities of the shell such as temperature, pressure and entropy are calculated for the final stage of black hole radiation.