# Black hole thermodynamics and heat engines in conformal gravity

## TL;DR

This paper explores the thermodynamics and heat engine efficiency of black holes in conformal gravity, revealing branched equations of state, bounded thermodynamic volume, and distinct efficiencies for different engine types.

## Contribution

It provides a detailed analysis of black hole thermodynamics in conformal gravity, highlighting unique features like branched EOS and efficiency bounds for heat engines.

## Key findings

- Black hole EOS in conformal gravity is always branched.
- Thermodynamic volume is bounded from above, affecting entropy.
- Efficiency of rectangular heat engines has a maximum value.

## Abstract

The extended phase space thermodynamics and heat engines for static spherically symmetric black hole solutions of four dimensional conformal gravity are studied in detail. It is argued that the equation of states (EOS) for such black holes is always branched, any continuous thermodynamical process cannot drive the system from one branch of the EOS into another branch. Meanwhile, the thermodynamical volume is bounded from above, making the black holes always super-entropic in one branch and may also be super-entropic in another branch in certain range of the temperature. The Carnot and Stirling heat engines associated to such black holes are shown to be distinct from each other. For rectangular heat engines, the efficiency always approaches zero when the rectangle becomes extremely narrow, and given the highest and lowest working temperatures fixed, there is always a maximum for the efficiency of such engines.