Thermodynamics of Quantum Field on the Kaluza-Klein Spacetime with Extra Fuzzy Geometry

We study the thermodynamics of quantum field on the spacetime with fuzzy geometry. The heat capacity of the quantum scalar field and Dirac field on the product of Minkowski spacetime by a fuzzy two-sphere is calculated. We see that the fermion capacity becomes a decreasing function of temperature in high-temperature limit, contrast to that always being an increasing function on the spacetime without the fuzzy geometry. We argue that the properties may be traced to the mechanism of “thermal reduction of the extra fuzzy space”. We also present a simple model to see such a mechanism.