Black Brane/Bose Gase Duality and Third Law of Thermodynamics

TL;DR

This paper extends the duality between black hole thermodynamics and Bose gases to black branes, showing that certain black branes obey the third law of thermodynamics and establishing a correspondence with non-relativistic Bose gases.

Contribution

It generalizes the black hole-Bose gas duality to black branes, linking their thermodynamics and entropy behavior across various spacetime dimensions and black brane types.

Findings

Black branes in AdS and Lifshitz spacetimes obey the third law.

Poincare black brane in D dimensions corresponds to a Bose gas in 2(D-2) dimensions.

Lifshitz branes relate to Bose gases with energy k^α in D-2 dimensions.

Abstract

In the thermodynamics of black holes in asymptotically flat space, the third law of thermodynamics is violated, and entropy cannot be consistently modeled through conventional statistical mechanics. Notably, the third law of thermodynamics is violated for the Schwarzschild black hole, and its entropy can only be described using an unconventional model, such as a Bose gas in negative dimensions. In contrast, for certain black brane solutions such as Poincare AdS black branes, Lifshitz black branes, and anisotropic Lifshitz-type black branes, the third law is preserved, with entropy vanishing as temperature approaches zero. In this paper, we extend the previously established duality between black hole and Bose gas thermodynamics to black branes. Specifically, the Poincare black brane in $D$ spacetime dimensions corresponds to a non-relativistic Bose gas in $2(D-2)$ spatial dimensions. Furthermore, the duality between Lifshitz branes and Bose gases relates a Lifshitz brane with exponent $\alpha$ in $D$-dimensional spacetime to a Bose gas of quasi-particles with energy $k^\alpha$ in $D-2$ spatial dimensions.