Black brane/Bose gas duality and the third law of thermodynamics

In the thermodynamics of black holes in an 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 the Bose gas in negative dimensions. In contrast, for certain black brane solutions, such as the Poincaré AdS black branes, Lifshitz black branes, and anisotropic Lifshitz-type black branes, the third law is preserved, with entropy vanishing as the temperature approaches zero. In this paper, we extend the previously established duality between black hole and Bose gas thermodynamics to black branes. Specifically, the Poincaré black brane in \(D\) spacetime dimensions corresponds to a nonrelativistic Bose gas in \(2(D-2)\) spatial dimensions. Furthermore, the duality between Lifshitz branes and Bose gases relates a Lifshitz brane with the exponent \(\alpha\) in \(D\)-dimensional spacetime to a Bose gas of quasiparticles with the energy \(k^\alpha\) in \(D-2\) spatial dimensions.