# A quantum Szilard engine without heat from a thermal reservoir

## TL;DR

This paper explores a quantum Szilard engine powered by measurements instead of heat, revealing fundamental limitations imposed by conservation laws and the WAY theorem on its operation.

## Contribution

It demonstrates the constraints on measurement-based quantum engines imposed by conservation laws, extending the understanding beyond thermally driven systems.

## Key findings

- The engine can operate without a thermal reservoir but must sacrifice measurement repeatability, weight entropy invariance, or universal work extraction.
- The limitations are derived from the Wigner-Araki-Yanase theorem, linking measurement constraints to fundamental physics.
- This work advances the development of thermodynamics-like principles for measurement-driven quantum systems.

## Abstract

We study a quantum Szilard engine that is not powered by heat drawn from a thermal reservoir, but rather by projective measurements. The engine is constituted of a system $\mathcal{S}$, a weight $\mathcal{W}$, and a Maxwell demon $\mathcal{D}$, and extracts work via measurement-assisted feedback control. By imposing natural constraints on the measurement and feedback processes, such as energy conservation and leaving the memory of the demon intact, we show that while the engine can function without heat from a thermal reservoir, it must give up at least one of the following features that are satisfied by a standard Szilard engine: (i) repeatability of measurements; (ii) invariant weight entropy; or (iii) positive work extraction for all measurement outcomes. This result is shown to be a consequence of the Wigner-Araki-Yanase (WAY) theorem, which imposes restrictions on the observables that can be measured under additive conservation laws. This observation is a first-step towards developing "second-law-like" relations for measurement-assisted feedback control beyond thermality.