Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?

TL;DR

This paper explores the fundamental resources needed for cooling quantum systems, unifying Landauer's principle with the third law of thermodynamics, and deriving limits on cooling protocols based on control complexity and thermodynamic constraints.

Contribution

It introduces a framework linking information-theoretic and thermodynamic limits on quantum cooling, including a new Carnot-Landauer limit for heat-engine-controlled protocols.

Findings

Perfect cooling with Landauer cost given infinite time or control complexity

Derivation of a Carnot-Landauer limit for heat-engine protocols

Protocols for saturating the thermodynamic bounds

Abstract

Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, which states that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilized? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure quantum states. We show that perfect cooling is possible with Landauer energy cost given infinite time or control complexity. However, such optimal protocols require complex unitaries generated by an external work source. Restricting to unitaries that can be run solely via a heat engine, we derive a novel Carnot-Landauer limit, along with protocols for its saturation. This generalizes Landauer's principle to a fully thermodynamic setting, leading to a unification with the third law and emphasizes the importance of control in quantum thermodynamics.