Treating the Rényi non-extensive parameter as a chemical potential can make Schwarzschild-de Sitter black holes locally and globally stable under fixed pressure and particle number.
Zeroth Law compatibility of non-additive thermodynamics
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Non-extensive thermodynamics was criticized among others by stating that the Zeroth Law cannot be satisfied with non-additive composition rules. In this paper we determine the general functional form of those non-additive composition rules which are compatible with the Zeroth Law of thermodynamics. We find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these. Our result offers a possible solution to the longstanding problem about equilibrium between extensive and non-extensive systems or systems with different non-extensivity parameters.
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Thermodynamic Stability of Schwarzschild-de Sitter Black holes with R\'enyi entropy
Treating the Rényi non-extensive parameter as a chemical potential can make Schwarzschild-de Sitter black holes locally and globally stable under fixed pressure and particle number.