# Vanishing efficiency of speeded-up quantum Otto engines

## TL;DR

This paper investigates the energy costs associated with shortcuts to adiabatic processes in quantum Otto engines, revealing that these costs lead to vanishing efficiency due to system-control interactions.

## Contribution

It clarifies the energy cost definition in quantum engines and demonstrates how it results in zero efficiency, highlighting the role of system-control interplay.

## Key findings

- Energy cost is identified as the exclusive work of the total system.
- Efficiency of the engine becomes zero due to these energy costs.
- Conditions for proportionality between primary and control system powers are established.

## Abstract

We assess the energy cost of shortcuts to adiabatic expansions or compressions of a harmonic oscillator, the power strokes of a quantum Otto engine. Difficulties to identify the cost stem from the interplay between different parts of the total system (the primary system -the particle-, and the control system) and definitions of work (exclusive and inclusive). While attention is usually paid to the inclusive work of the primary system, we identify the energy cost as the exclusive work of the total system, which, for a clearcut scale disparity between primary and control systems, coincides with the exclusive work for the control system. This energy cost makes the efficiency of the engine zero. For an ion in a Paul trap, the Paul trap fixes the gauge for the primary system, resulting in a counterintuitive evolution of its inclusive power and internal energy. Conditions for which inclusive power of the primary system and exclusive power control system are proportional are found.