Non-commutative correction of ideal gas thermodynamics

In this study, we investigate the thermodynamics of a relativistic ideal gas within the context of κ -deformed space–time and Rainbow gravity background. To achieve this, we construct a modified partition function by considering a deformed Hamiltonian and incorporating corrections based on the time-invariant phase-space volume. We explore the implications of our model on the modified black body radiation spectrum and the modified Debye theory of specific heat in κ -deformed space–time and Rainbow gravity background.