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Abstract
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.
Highlights
There have been several intriguing connections between gravity and thermodynamics discovered over the past few years, a better understanding of which necessitates study of thermal systems in presence of gravity
It is more useful to ask whether a quantum mechanical calculation can give any new information, which is the question we hope to address in this note in the context of one of the simplest thermodynamic systems – a box of ideal gas
We find that all thermodynamic quantities acquire a specific correction term which is independent of system details such as box dimensions and mass of particles
Summary
There have been several intriguing connections between gravity and thermodynamics discovered over the past few years (see [1] for a recent review), a better understanding of which necessitates study of thermal systems in presence of gravity. It is more useful to ask whether a quantum mechanical calculation can give any new information, which is the question we hope to address in this note in the context of one of the simplest thermodynamic systems – a box of ideal gas. We consider such a box of ideal gas in an arbitrary curved spacetime, with its center freely falling along a geodesic with 4-velocity u, and compute corrections to the partition function due to spacetime curvature. In order-ofmagnitude arguments, we will use R to denote typical magnitude of curvature tensor components
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