Thermodynamics of Ideal Gas on the Spacetime with Noncommutative Geometry

We investigate the thermodynamics of ideal gas on the spacetime with noncommutative fuzzy geometry. We first find that the heat capacity of the ideal boson and fermion on the fuzzy two-sphere have different values, contrast to that on the commutative geometry, and see that the heat capacity approaches to zero in high-temperature limit. We next evaluate the heat capacity of the ideal boson and fermion on the product of 1+D Minkowski spacetime by a fuzzy two-sphere and find that the heat capacity approaches 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 extra fuzzy space”. *E-mail: [email protected]