Is quantum uncertainty principle related to thermodynamics?

Would like to ask a question, but first i would like to say Hello Everybody in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question.

The uncertainty principle in quantum mechanics is well known and considered one of most basic properties of natural reality. The 2nd Law of thermodynamics is also well known and also considered one of the most basic processes of natural reality.

The uncertainty principle uses and is related to Planck's constant. Planck's constant has the dimensions of action and in a statistical mechanics approach, also relates nicely with the partitioning of the phase-space providing the basic measure for the entropy functional (this answer provides a nice outline of this).

Apart from that, there are relatively recent papers which relate the Heisenberg Uncertainty Principle in quantum mechanics directly and intuitively to the 2nd Law of Thermodynamics.

Is this relation correct? And if so can we derive one from the other?

Thank you

PS. One can also check this question, which although not the same, is related in an interesting way.

UPDATE:

anna's answer is accepted since by mentioning the derivation of (part of) the 2nd law from unitary dynamics, answers the question at least in one way. Please consider this as still open so you can add another answer. There are more alternatives (and one of which is my stance, ie thermodynamics -> uncertainty)

Answer

You say your self :

The uncertainty principle in quantum mechanics is well known and considered one of most basic properties of natural reality.

In fact quantum mechanics and its postulates and laws are the underlying framework on which any classical theory is built.

The "laws" of classical theories emerge from the underlying quantum mechanical framework. In the paper you quote they claim that :

More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.

As an experimentalist I am in no position to check whether their conclusion is correct, this is the work of peer review in journals, and it has been accepted in Nature and , I hope, peer reviewed. Well done if it is correct, because it is one more validation of the underlying quantum mechanical framework.

I do not know whether it is related to the statement in the wiki article :

In statistical thermodynamics, the second law is a consequence of unitarity in quantum mechanics

It seems from the references to be connected to the many worlds interpretation , so this new derivation might be a more mainstream connection of the quantum mechanical framework to the second law.