Heat engines for scale invariant systems dual to black holes

According to holography, a black hole is dual to a thermal state in a strongly coupled quantum system. One of the best-known examples of holography is the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Despite extensive work on holographic thermodynamics, heat engines for CFT thermal states have not been explored. We construct reversible heat engines where the working substance consists of a static thermal equilibrium state of a CFT. For thermal states dual to an asymptotically AdS black hole, this yields a realization of Johnson’s holographic heat engines. We compute the efficiency for a number of idealized heat engines, such as the Carnot, Brayton, Otto, Diesel, and Stirling cycles. The efficiency of most heat engines can be derived from the CFT equation of state, which follows from scale invariance, and we compare them to the efficiencies for an ideal gas. However, the Stirling efficiency for a generic CFT is uniquely determined in terms of its characteristic temperature and volume only in the high-temperature or large-volume regime. We derive an exact expression for the Stirling efficiency for CFT states dual to AdS-Schwarzschild black holes and compare the subleading corrections in the high-temperature regime with those in a generic CFT. Holography suggests that black holes correspond to thermal states in strongly coupled quantum systems, presenting a unique opportunity to explore gravitational physics via thermodynamic processes. The authors construct reversible heat engines using conformal field theory states, deriving efficiencies and revealing insights into holographic heat engines, particularly for Stirling cycles in high-temperature regimes.