Sigh. There is no link to a peer reviewed paper in there, just describing entropy and a few scientists working on describing thermodynamics via quantum theory.
Then this paper applied constructor theory to form a constructor theory of information:
Deutsch David and Marletto Chiara 2015 Constructor theory of information Proc. R. Soc. A.4712014054020140540
(Download: https://royalsocietypublishing.org/doi/10.1098/rspa.2014.054...)
Finally, this paper applied the constructor theories of information and probability to thermodynamics:
https://arxiv.org/pdf/1608.02625.pdf
(not yet published in a journal, to my knowledge)
It appears that the first occurrence of the the name of each of the researchers mentioned in the article links through to their respective home-page. At a quick glance, most of them appear to publish lists of their publications, some with direct links to the actual papers. Of course it might be hard to tease out which papers they've contributed to that pertain to this specific topic, but it would probably be worth the effort for someone who was really interested.
It would be nice, but I think this is a survey of an evolving field and there probably isn't any one pivotal paper. Plugging some key names (Marletto, Halpern) and key terms (constructor theory, resource theory) from the article into Google Scholar, or visiting the linked researchers' websites, will probably get you what you're looking for.
David Deutsch as well. Chiara Marleto has a nice recent book, The Science of Can and Can't, which discusses briefly the Second Law in the context of constructor theory.
"(2022) Emergence of Constructor-Based Irreversibility in Quantum Systems:
Theory and Experiment, Marletto & Vedral"
That's related to this quote from the article:
> "But crucially, the theory also predicts that the row becomes even less able to do the reverse transformation from B2 to B1. The researchers have confirmed this prediction experimentally using photons for B and a fiber optic circuit to simulate a row of three qubits."
The experiment is rather complex, and would take a long time to analyze and understand in depth. They appear to be claiming that microscopic reversibility, a cornerstone of atomic-molecular kinetic theory, is being violated in their setup? Seems like a rather extraordinary claim but it passed peer review in a major journal so, worth digging into probably.
For those who want an introductory overview of the issue, this is a good one:
The laws of thermodynamics do not particularly concern themselves with the specific how and why of heat transfer, which makes sense for laws that were formulated before the atomic theory was fully adopted. They deal with the sum total of energy and heat transitions within a system and do not take into account the specific nature of heat transference on the atomic or molecular level."
In practice the second law is not all that useful although it's philosophically important I suppose. For example, a redwood tree growing from a redwood seed plus simple inputs (CO2, H2O, photons, NH3 etc.) is clearly a local decrease in entropy, as opposed to the dispersal of those elements when a redwood tree burns or falls and is digested by fungi, but since solar fusion is creating a much greater increase in entropy, there are no second law violations. Similarly the creation of heavy elements in a supernova would seem to be a decrease in entropy but the release of all that energy to the surrounding universe ensures no second law violations take place. In practice it's very difficult to do all the accounting for even moderately complex systems.
