The main objective of this talk is to identify black hole solutions that satisfy the third law of thermodynamics. We begin by examining the possibility of finding such solutions within the Einstein–Maxwell–Dilaton models with purely electric, purely magnetic, and electric–magnetic configurations coupled through two independent exponential coupling functions and subsequently analyze their thermodynamic properties. Our primary focus will be on anisotropic Lifshitz and hyperscaling Lifshitz solutions. It was found that for this model, the third law of thermodynamics is valid, while for most ordinary black holes, such as Schwarzschild, rotating, and charged black hole solutions, the third law of thermodynamics is violated.

We establish a duality between the Bose gas and these black brane solutions. This duality provides a statistical description of black hole entropy for various dimensions and anisotropy parameters. Our framework enables the construction of a microscopic statistical description of entropy for a broad class of non-extremal black holes through a generalization of the holographic duality approach. We demonstrate that anisotropy parameters serve as natural regulators of black hole/Bose gas duality.

The first part of the talk is based on the joint paper, "Black brane/Bose gas duality and the third law of thermodynamics", Irina Aref'eva, Igor Volovich, Daniil Stepanenko , 2411.01778 [hep-th], published in Teor.Mat.Fiz. 222 (2025) 2, 276-284, Theor.Math.Phys. 222 (2025) 2, 276-284.