# An Exact Model of the Power/Efficiency Trade-Off While Approaching the Carnot Limit

## TL;DR

This paper presents an exactly solvable model demonstrating how heat engines can approach Carnot efficiency while maintaining finite power, based on extended thermodynamics inspired by charged black holes.

## Contribution

It introduces a novel, exactly solvable model that explores the power/efficiency trade-off near the Carnot limit, rooted in black hole thermodynamics.

## Key findings

- Model shows finite power at near-Carnot efficiency
- Provides insights into thermodynamic mechanisms of black hole-inspired engines
- Serves as a theoretical laboratory for studying efficiency limits

## Abstract

The Carnot heat engine sets an upper bound on the efficiency of a heat engine. As an ideal, reversible engine, a single cycle must be performed in infinite time, and so the Carnot engine has zero power. However, there is nothing in principle forbidding the existence of a heat engine whose efficiency approaches that of Carnot while maintaining finite power. Such an engine must have very special properties, some of which have been discussed in the literature, in various limits. While recent theorems rule out a large class of engines from maintaining finite power at exactly the Carnot efficiency, the approach to the limit still merits close study. Presented here is an exactly solvable model of such an approach that may serve as a laboratory for exploration of the underlying mechanisms. The equations of state have their origins in the extended thermodynamics of electrically charged black holes.