Thermodynamics on Fuzzy Spacetime

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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.