Generalized Maxwell equal area law and black holes in complex free energy

Abstract

Maxwell equal area law is an important and traditional analytical tool in thermodynamic phase transition, especially in the calculation of gas-liquid phase transition, which reconciles the theoretical calculation with the experimental results. Undoubtedly, its importance is also self-evident for the black hole thermodynamic system. In this study, we construct a generalized Maxwell equal area law, which allows different states of thermodynamic systems to be within the generalized free energy. The black hole thermodynamic characteristics are spontaneously emerged in the free energy landscape. Furthermore, by analytic continuation, we utilize the properties of analytical functions to investigate some universal characteristics of thermodynamic phase transitions in black holes, and preliminarily establish the counterpart of thermodynamic phase transitions in the complex domain.

v1:6 pages, 3 figures; v2: add References and some comments; v3: title changed and clarifications added; v4: to be published in PLB;

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• Thermodynamic topological classes of the rotating, accelerating black holes
• Thermodynamic phase transition rate for the third-order Lovelock black hole in diverse dimensions
• Thermodynamic phase transition and winding number for the third-order Lovelock black hole
• Kramer's Escape Rate and Phase Transition Dynamics in AdS Black Holes
• Thermodynamic bounce effect in quantum BTZ black hole
• Riemann Surfaces and Winding Numbers of Rényi Phase Structure of Charged-Flat Black Holes
• Topology of black hole thermodynamics: A brief review
• The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases
• Black hole thermodynamic free energy as $A$-discriminants