  We investigate the thermodynamics of non-relativistic and relativistic ideal
gases on the spacetime with noncommutative fuzzy geometry. We first find that
the heat capacities of the non-relativistic ideal boson and fermion on the
fuzzy two-sphere have different values, contrast to that on the commutative
geometry. We calculate the "statistical interparticle potential" therein and
interprete this property as a result that the non-commutativity of the fuzzy
sphere has an inclination to enhance the statistical "attraction (repulsion)
interparticle potential" between boson (fermion). We also see that at high
temperature the heat capacity approaches to zero. We next evaluate the heat
capacities of the non-relativistic ideal boson and fermion on the product of
the 1+D (with D=2,3) Minkowski spacetime by a fuzzy two-sphere and see that the
fermion capacity could be a decreasing function of temperature in
high-temperature limit, contrast to that always being an increasing function on
the commutative geometry. Also, the boson and fermion heat capacities both
approach to that on the 1+D Minkowski spacetime in high-temperature limit. We
discuss these results and mention that the properties may be traced to the
mechanism of "thermal reduction of the fuzzy space". We also investigate the
same problems in the relativistic system with free Klein-Gordon field and Dirac
field and find the similar properties.
