Second laws under control restrictions

TL;DR

This paper generalizes the second law of thermodynamics to scenarios with limited control over quantum systems, revealing how control restrictions impact work extraction and the fundamental bounds in realistic quantum thermodynamic processes.

Contribution

It derives a new second law applicable under arbitrary control restrictions and applies it to practical scenarios like energy gap limitations and local control in many-body systems.

Findings

Limited control reduces maximum extractable work.

Optimal work extraction differs from thermal contact in restricted scenarios.

Results extend second law to practical quantum thermodynamics.

Abstract

The second law of thermodynamics, formulated as an ultimate bound on the maximum extractable work, has been rigorously derived in multiple scenarios. However, the unavoidable limitations that emerge due to the lack of control on small systems are often disregarded when deriving such bounds, which is specifically important in the context of quantum thermodynamics. Here, we study the maximum extractable work with limited control over the working system and its interaction with the heat bath. We derive a general second law when the set of accessible Hamiltonians of the working-system is arbitrarily restricted. We then apply our bound to particular scenarios that are important in realistic implementations: limitations on the maximum energy gap and local control over many-body systems. We hence demonstrate in what precise way the lack of control affects the second law. In particular, contrary to the unrestricted case, we show that the optimal work extraction is not achieved by simple thermal contacts. Our results do not only generalize the second law to scenarios of practical relevance, but also take first steps in the direction of local thermodynamics.