# Relativistic quantum heat engine from uncertainty relation standpoint

## TL;DR

This paper introduces a relativistic quantum heat engine model using a particle in a potential well, linking thermodynamic efficiency bounds to quantum uncertainty relations, and explores its work and efficiency characteristics.

## Contribution

It develops a novel relativistic quantum heat engine model based on uncertainty relations, extending quantum thermodynamics to relativistic regimes.

## Key findings

- Bounds on efficiency derived from thermal uncertainty relations
- Work extraction analyzed for relativistic quantum systems
- Efficiency limits established through quantum uncertainty principles

## Abstract

Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.