  Existence of minimal length is suggested in any quantum theory of gravity
such as string theory, double special relativity and black hole physics. One
way to impose minimal length is deforming Heisenberg algebra in phase space
which is called Generalized Uncertainty Principle (GUP). In this paper, we
develop statistical mechanics in GUP framework. Our method is quite general and
does not need to fix the generalized coordinates and momenta. We define general
transformation in phase space which transforms usual Heisenberg algebra to a
deformed one. In this method, quantum gravity effects only acts on the
structure of phase space and we relate these effects to the density of states.
We find an interesting phenomenon in Maxwell-Boltzmann statistics which has not
a classical analogy. We show that there is an upper bound for the number of
excited particles in the limit of high temperature which implies to the
condensation. Also we study modification of Bose-Einstein condensation and the
completely degenerate gas.
