It seems as though the authors are confusing Boltzmann's H-theorem and its cousins expressed in more complicated formalisms with the Second law of thermodynamic

It seems as though the authors are confusing Boltzmann's H-theorem and its cousins expressed in more complicated formalisms with the Second law of thermodynamics. That's a very common misconception, often resulting in announces of apparently great discoveries, while the sober account would be more akin to "we derived a theorem where this special expression, similar to Boltzmann's H-function, does not behave as one would expect based on the H-theorem, which in turn is proven to be valid only for a simplified model of ideal gas in special condition." Not so interesting. Second law is an experimental law that concerns macroscopic systems. So far, this law was not shown to be violated based on any broadly accepted theory.