# Thermodynamic Geometry of Microscopic Heat Engines

## TL;DR

This paper introduces a geometric framework for analyzing microscopic heat engines, revealing universal efficiency-power trade-offs and quantum coherence effects, with practical examples in solid-state systems.

## Contribution

It develops a unified geometric approach applicable to both classical and quantum microscopic heat engines, highlighting quantum coherence's impact on performance.

## Key findings

- Universal trade-off relation between efficiency and power derived from geometry.
- Quantum coherence reduces engine performance regardless of driving strength.
- Single-qubit heat engine example demonstrates practical relevance.

## Abstract

We develop a geometric framework to describe the thermodynamics of microscopic heat engines driven by slow periodic temperature variations and modulations of a mechanical control parameter. Covering both the classical and the quantum regime, our approach reveals a universal trade-off relation between efficiency and power that follows solely from geometric arguments and holds for any thermodynamically consistent microdynamics. Focusing on Lindblad dynamics, we derive a second bound showing that coherence as a genuine quantum effect inevitably reduces the performance of slow engine cycles regardless of the driving amplitudes. To demonstrate the practical applicability of our results, we work out the example of a single-qubit heat engine, which lies within the range of current solid-state technologies.