We study the \textit{quantum} partition function of non-relativistic, ideal gas in a (non-cubical) box falling freely in arbitrary curved spacetime with centre 4-velocity u^a. 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 \textit{kinematic} details such as box dimensions and mass of particles. This term is characterized by the dimensionless quantity, Ξ=R_00 Λ^2, where R_00=R_ab u^a u^b and Λ=β\hbar c, and, quite intriguingly, produces Euler relation of homogeneity two between entropy and energy -- a relation familiar from black hole thermodynamics.

5 pages, no figures; abstract abridged and an appendix added outlining some relevant mathematical steps; accepted in Phys. Lett. B