Box of Ideal Gas in Free Fall

الأصل · EN

We study the quantum partition function of non-relativistic, ideal gas in a (non-cubical) box falling freely in arbitrary curved spacetime with centre 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=R₀0 Λ², where R₀0=Rₐb uᵃ uᵇ and Λ=βℏ c, and, quite intriguingly, produces Euler relation of homogeneity two between entropy and energy -- a relation familiar from black hole thermodynamics.