Basically, Nernst's Heat Theorem (hereafter, NHT for short) states that as the temperature of a system approaches absolute zero, then so does its entropy, and this provides a reason why absolute zero is unattainable in practice.

However, whilst this was used by Max Planck as the basis of the Third Law of Thermodynamics, there are problems with NHT as it stands, namely, that it depends upon assumptions that may possibly not hold.

Now, two authors of a Nature Communications paper at University College, London, have applied quantum information theory to the problem, and generated a mathematical result that places the NHT on a rigorous foundation.

The paper in question is this one:

A General Derivation And Quantification Of The Third Law Of Thermodynamics by Lluis Masanes & Jonathan Oppenheim, Nature Communications, 8: 14538 DOI: 10.1038/ncomms14538 (14th March 2017) [Full paper downloadable from here]

Masanes & Oppenheim, 2017 wrote:Abstract

The most accepted version of the third law of thermodynamics, the unattainability principle, states that any process cannot reach absolute zero temperature in a finite number of steps and within a finite time. Here, we provide a derivation of the principle that applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any temperature, and translate these resources into the minimal time or number of steps, by considering the notion of a thermal machine that obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our results also clarify the connection between two versions of the third law (the unattainability principle and the heat theorem), and place ultimate bounds on the speed at which information can be erased.

This, by the way, is a paper in which the Supplementary Information is vital, and this can be downloaded from here.