# Quantum mechanical bound for efficiency of quantum Otto heat engine

## TL;DR

This paper derives a quantum mechanical efficiency bound for a quantum Otto heat engine with a harmonic oscillator, showing it can be tighter than the Carnot limit due to quantum effects.

## Contribution

It introduces an $$-dependent quantum efficiency bound for the quantum Otto engine, extending thermodynamic limits with quantum considerations.

## Key findings

- The quantum efficiency bound is tighter than Carnot efficiency.
- Quantum effects can suppress heat engine performance.
- The bound is achieved at low temperatures where quantum effects dominate.

## Abstract

The second law of thermodynamics constrains that the efficiency of heat engines, classical or quantum, cannot be greater than the universal Carnot efficiency. We discover another bound for the efficiency of a quantum Otto heat engine consisting of a harmonic oscillator. Dynamics of the engine is governed by the Lindblad equation for the density matrix, which is mapped to the Fokker-Planck equation for the quasi-probability distribution. Applying stochastic thermodynamics to the Fokker-Planck equation system, we obtain the $\hbar$-dependent quantum mechanical bound for the efficiency. It turns out that the bound is tighter than the Carnot efficiency. The engine achieves the bound in the low temperature limit where quantum effects dominate. Our work demonstrates that quantum nature could suppress the performance of heat engines in terms of efficiency bound, work and power output.