The zeroth law in quasi-homogeneous thermodynamics and black holes

Abstract

Motivated by black holes thermodynamics, we consider the zeroth law of thermodynamics for systems whose entropy is a quasi-homogeneous function of the extensive variables. We show that the generalized Gibbs-Duhem identity and the Maxwell construction for phase coexistence based on the standard zeroth law are incompatible in this case. We argue that the generalized Gibbs-Duhem identity suggests a revision of the zeroth law which in turns permits to reconsider Maxwell's construction in analogy with the standard case. The physical feasibility of our proposal is considered in the particular case of black holes.

8 pages, 7 figures

References in corpus (7)

• Black hole chemistry: thermodynamics with Lambda
• Zeroth Law compatibility of non-additive thermodynamics
• Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes
• Black holes and Boyle's law -- the thermodynamics of the cosmological constant
• Violation of the Zeroth Law of Thermodynamics in Systems with Negative Specific Heat
• Coexistence curves and molecule number densities of AdS black holes in the reduced parameter space
• Vacuum energy and the latent heat of AdS-Kerr black holes

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• Reparametrizations and metric structures in thermodynamic phase space