Box of Ideal Gas in Free Fall
Abstract
We study the \textit{quantum} partition function of nonrelativistic, ideal gas in a (noncubical) box falling freely in arbitrary curved spacetime with centre 4velocity u^a. When perturbed energy eigenvalues are properly taken into account, we find that corrections to various thermodynamic quantities include a very specific, subdominant 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 arXiv:
 arXiv:1108.6301
 Bibcode:
 2011arXiv1108.6301K
 Keywords:

 General Relativity and Quantum Cosmology;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 5 pages, no figures