Cooling to absolute zero: The unattainability principle

TL;DR

This paper reviews various derivations of the unattainability principle, illustrating that reaching absolute zero temperature requires infinite resources or time, based on different operational assumptions in thermodynamics and quantum refrigeration models.

Contribution

It compares derivations of the unattainability principle under broad and specific operational frameworks, highlighting the resource requirements for approaching absolute zero.

Findings

Perfect cooling demands infinite resources.

Infinite time is necessary to reach absolute zero.

Derivations apply to both general and experimental models.

Abstract

The unattainability principle (UP) is an operational formulation of the third law of thermodynamics stating the impossibility to bring a system to its ground state in finite time. In this work, several recent derivations of the UP are presented, with a focus on the set of assumptions and allowed sets of operations under which the UP can be formally derived. First, we discuss derivations allowing for arbitrary unitary evolutions as the set of operations. There the aim is to provide fundamental bounds on the minimal achievable temperature, which are applicable with almost full generality. These bounds show that perfect cooling requires an infinite amount of a given resource -- worst-case work, heat bath's size and dimensionality or non-equilibrium states among others -- which can in turn be argued to imply that an infinite amount of time is required to access those resources. Secondly, we present derivations within a less general set of operations conceived to capture a broad class of currently available experimental settings. In particular, the UP is here derived within a model of linear and driven quantum refrigerators consisting on a network of harmonic oscillators coupled to several reservoirs at different temperatures.