Dispersion relation, black hole thermodynamics and generalization of uncertainty principle

In a heuristic manner, we discuss the effect of the modified dispersion relation (MDR) on the thermodynamics of a Schwarzschild black hole (including the corrections to black hole temperature and entropy). Different from the generalized uncertainty principle (GUP), the linear-in-lp term of MDR provides a correction of order of the square root of the black hole area, besides a logarithmic correction. MDR may be constrained to a certain extent. The relation between MDR and GUP is also discussed.