Box of ideal gas in free fall

We study the quantum partition function of non-relativistic, ideal gas in a (non-cubical) box falling freely in arbitrary curved spacetime with center 4-velocity ua. When perturbed energy eigenvalues are properly taken into account, we find that corrections to various thermodynamic quantities include a very specific, sub-dominant term which is independent of kinematic details such as box dimensions and mass of particles. This term is characterized by the dimensionless quantity, Ξ=R0ˆ0ˆΛ2, where R0ˆ0ˆ=Rabuaub and Λ=βℏc, and, quite intriguingly, produces Euler relation of homogeneity two between entropy and energy - a relation familiar from black hole thermodynamics.