Work extractability from energy eigenstates under optimized local operations

TL;DR

This paper investigates how the extractability of work from energy eigenstates in quantum many-body systems depends on system integrability, revealing fundamental differences in thermodynamic behavior between integrable and nonintegrable systems.

Contribution

It demonstrates that integrability determines the number of work-extractable eigenstates, providing new insights into quantum thermodynamics and the second law in many-body systems.

Findings

Nonintegrable systems have nearly zero work-extractable eigenstates.

Integrable systems possess exponentially many work-extractable eigenstates.

Athermal eigenstates are key to understanding work extractability differences.

Abstract

We examine the relationship between the second law of thermodynamics and the energy eigenstates of quantum many-body systems that undergo cyclic unitary evolution. Using a numerically optimized control protocol, we analyze how the work extractability is affected by the integrability of the system. Our findings reveal that, in nonintegrable systems the number of work-extractable energy eigenstates converges to zero, even when the local control operations are optimized. In contrast, in integrable systems, there are exponentially many eigenstates from which positive work can be extracted, regardless of the locality of the control operations. We numerically demonstrate that such a strikingly different behavior can be attributed to the number of athermal energy eigenstates. Our results provide insights into the foundations of the second law of thermodynamics in isolated quantum many-body systems, which are expected to contribute to the development of quantum many-body heat engines.