Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-08-31
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages, no figures; abstract formatted (see PDF file)
Scientific paper
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 u^a. Using perturbed energy eigenvalues to evaluate the canonical partition function, we find that corrections to various thermodynamic quantities such as mean energy, entropy and specific heat include a very specific, sub-dominant term characterized by the dimensionless quantity, X = R_00 q^2, where R_00 = R_ab u^a u^b and q = \beta \hbar c. This X-contribution does not depend on kinematic details of the system such as box dimensions and mass of particles, and in particular leads to S_X = (1/2) \beta U_X (see text), a relation familiar from black hole thermodynamics. What is curious is that our result depends crucially on quantum mechanics since, in effect, the gas is allowed to "feel" the presence of the box through use of unperturbed wave function satisfying appropriate boundary conditions at the box walls. This is the feature which a classical analysis will completely miss. Our result might bear relevance in several contexts, such as analyses related to the generalized second law, a better understanding of horizon thermodynamics, and the "emergent gravity" viewpoint.
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