An Exact Efficiency Formula for Holographic Heat Engines

TL;DR

This paper derives an exact and general efficiency formula for holographic heat engines, especially black hole engines, using a geometric approach that simplifies calculations and extends to broader classes of heat engines.

Contribution

It introduces a simple efficiency formula for black hole heat engines and develops a geometric algorithm applicable to various heat engine types beyond black holes.

Findings

Efficiency can be expressed in terms of black hole mass at cycle corners.

A geometric algorithm approximates arbitrary cycles with rectangles.

The method extends beyond black hole thermodynamics.

Abstract

Further consideration is given to the efficiency of black hole heat engines that perform mechanical work via the pdV terms present in the First Law of extended gravitational thermodynamics. It is noted that when the engine cycle is a rectangle with sides parallel to the (p,V) axes, the efficiency can be written simply in terms of the mass of the black hole evaluated at the corners. Since an arbitrary cycle can be approximated to any desired accuracy by a tiling of rectangles, a general geometrical algorithm for computing the efficiency follows. A simple generalization of the algorithm renders it applicable to more general classes of heat engine, beyond the black hole context.