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GUP deformed phase-space and axiomatic thermodynamic self-consistency

Based on the generalized uncertainty principle (GUP) with a deformation of the phase-space, the partition function has recently been modified. In the present work, we analyze the self-consistency of the axiomatic thermodynamics derived from the deformed partition function. First, we set up the thermodynamic quantities such as pressure, energy density, entropy and number density, then we extend the study for testing the approval of consistency. We found that the deformed phase-space satisfies the axiomatic self-consistency of thermodynamics. We would expect the effects of GUP to be more pronounced at high frequencies, but the used deformed phase-space factor would still diverge as [Formula: see text] approaches [Formula: see text].