Box of Ideal Gas in Free Fall
Abstract
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, \Xi=R_00 \Lambda^2, where R_00=R_ab u^a u^b and \Lambda=\beta \hbar c, and, quite intriguingly, produces Euler relation of homogeneity two between entropy and energy -- a relation familiar from black hole thermodynamics.
Keywords
Cite
@article{arxiv.1108.6301,
title = {Box of Ideal Gas in Free Fall},
author = {Dawood Kothawala},
journal= {arXiv preprint arXiv:1108.6301},
year = {2013}
}
Comments
5 pages, no figures; abstract abridged and an appendix added outlining some relevant mathematical steps; accepted in Phys. Lett. B