de Sitter Black Holes, Schottky Peaks, and Continuous Heat Engines

Recent work has uncovered Schottky-like peaks in the temperature dependence of key specific heats of certain black hole thermodynamic systems. They signal a finite window of available energy states for the underlying microscopic degrees of freedom. This paper reports on new families of peaks, found for the Kerr and Reissner-Nordstrom black holes in a spacetime with positive cosmological constant. It is known that a system with a highest energy, when coupled to two distinct heat baths, can naturally generate a thermodynamic instability, population inversion, a channel for work output. It is noted that these features are all present for de Sitter black holes. It is shown that there are trajectories in parameter space where they behave as generalized masers, operating as continuous heat engines, doing work by shedding angular momentum. It is suggested that bounds on efficiency due to the second law of thermodynamics for general de Sitter black hole solutions could provide powerful consistency checks.
Comment: v1:- 18 pages, multiple figures, one trumpet; v2:- 22 pages. Improved discussion (with new refs and figures), including clarification about role of Penrose processes. v3: key sign error in first law found. Strengthens definition of heat engine paths