  A possible discrepancy has been found between the results of a neutron
interferometry experiment and Quantum Mechanics. This experiment suggests that
the weak equivalence principle is violated at small length scales, which
quantum mechanics cannot explain. In this paper, we investigated whether the
Generalized Uncertainty Principle (GUP), proposed by some approaches to quantum
gravity such as String Theory and Doubly Special Relativity Theories (DSR), can
explain the violation of the weak equivalence principle at small length scales.
We also investigated the consequences of the GUP on the Liouville theorem in
statistical mechanics. We have found a new form of invariant phase space in the
presence of GUP. This result should modify the density states and affect the
calculation of the entropy bound of local quantum field theory, the
cosmological constant, black body radiation, etc. Furthermore, such
modification may have observable consequences at length scales much larger than
the Planck scale. This modification leads to a \sqrt{A}-type correction to the
bound of the maximal entropy of a bosonic field which would definitely shed
some light on the holographic theory.
