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=R0̂0̂Λ2, where R0̂0̂=Rabuaub and Λ=βℏc, and, quite intriguingly, produces Euler relation of homogeneity two between entropy and energy - a relation familiar from black hole thermodynamics. © 2013 Elsevier B.V.

Dawood Kothawala

Department Of Physics

Fulltext

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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

There is a considerable amount of evidence to suggest that the field equations of gravity have the same status as, say, the equations describing an emergent phenomenon like elasticity. In fact, it is possible to derive the field equations from a thermodynamic variational principle in which a set of normalized vector fields are varied rather than the metric. We show that this variational principle can arise as a low-energy [LP=(G/c3)1/2→0] relic of a plausible nonperturbative effect of quantum gravity, viz. the existence of a zero-point length in the spacetime. Our result is nonperturbative in the following sense: If we modify the geodesic distance in a spacetime by introducing a zero-point length, to incorporate some effects of quantum gravity, and take the limit LP→0 of the Ricci scalar of the modified metric, we end up getting a nontrivial, leading order (LP-independent) term. This term is identical to the expression for entropy density of spacetime used previously in the emergent gravity approach. This reconfirms the idea that the microscopic degrees of freedom of the spacetime, when properly described in the full theory, could lead to an effective description of geometry in terms of a thermodynamic variational principle. This is conceptually similar to the emergence of thermodynamics from the mechanics of, say, molecules. The approach also has important implications for the cosmological constant which are briefly discussed. © 2014 American Physical Society.

Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
ISSN	03702693
Open Access	No