In order to establish under which conditions specific results from black hole thermodynamics hold, it is important to know which assumptions were made on the thermodynamic theory. This can be accomplished through the use of a rigorous phenomenological axiomatic framework, such at that proposed by Kammerlander [1]. However, existing frameworks only consider energy as a conserved quantity. This means that the applicability of these frameworks to systems which have multiple conserved quantities is limited. As black holes have internal angular momentum and charge, this limitation also extends to them. In this work, we address this by extending Kammerlander's framework to describe multiple conserved quantities.

To do so, we first consider microscopic thermodynamics to extend Kammerlander's framework and then to verify our generalisations. Next, we apply our extended framework to black holes, and we successfully confirm all previously established results which we took under consideration.

[1] Philipp Kammerlander. Tangible Phenomenological Thermodynamics. PhD thesis, ETH Zurich, 2019