# Relativistic Quantum Otto Engine: Generalized efficiency bounds and frictional effects

## TL;DR

This paper explores the efficiency limits of a relativistic quantum Otto engine with a harmonic oscillator, deriving analytical bounds considering relativistic effects and nonadiabatic driving, and highlighting the impact of frictional effects.

## Contribution

It provides the first systematic analysis of how relativistic motion and nonadiabatic effects influence quantum heat engine efficiency bounds.

## Key findings

- Derived a generalized Carnot efficiency incorporating relativistic effects.
- Established a maximum efficiency limit of 1/2 for nonadiabatic protocols.
- Presented analytical expressions for efficiency bounds in sudden-switch protocols.

## Abstract

This work investigates a relativistic quantum Otto engine with a harmonic oscillator as its working medium, analyzing how relativistic motion and nonadiabatic driving affect its performance and efficiency bounds. In the adiabatic regime, a closed-form analytical expression is derived for the generalized Carnot efficiency, which incorporates the effects of relativistic motion and reduces to the standard Carnot efficiency in the nonrelativistic limit. For nonadiabatic driving, we consider sudden compression and expansion work strokes and show that the maximum efficiency achievable by the engine is limited to 1/2, even in the ultra-relativistic limit. Going one step further, we also derive an analytical expression for the efficiency bound in the sudden-switch protocol, which can be regarded as the nonadiabatic counterpart of the generalized Carnot efficiency. Together, these results provide analytical bounds for the efficiency of relativistic quantum heat engines and constitute the first systematic study of the interplay between relativistic motion and frictional effects arising from nonadiabatic driving.