Heat engines for scale invariant systems dual to black holes

TL;DR

This paper constructs and analyzes holographic heat engines using thermal states of conformal field theories dual to black holes, exploring their efficiencies across various thermodynamic cycles and regimes.

Contribution

It introduces the concept of holographic heat engines for CFT thermal states and derives efficiency formulas, including an exact expression for the Stirling cycle in AdS-Schwarzschild backgrounds.

Findings

Efficiency formulas depend on the CFT equation of state and scale invariance.

Most efficiencies can be compared to ideal gas benchmarks.

High-temperature regime simplifies the Stirling efficiency expression.

Abstract

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.