Box of Ideal Gas in Free Fall

TL;DR

This paper investigates the quantum thermodynamics of an ideal gas in a freely falling box within curved spacetime, revealing a universal correction term linked to black hole thermodynamics.

Contribution

It introduces a novel correction to thermodynamic quantities that is independent of kinematic details and relates to black hole entropy-energy relations.

Findings

Identifies a specific correction term characterized by =R_00 \u03b3^2.

Shows the correction leads to an Euler relation similar to black hole thermodynamics.

Demonstrates the correction's universality across different box geometries.

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.