[grungegun]

It looks like in the results section eqs (8)-(13), they give the main thrust of their idea. To demonstrate that not all machines are reversible they have to take the limit of the number of qubits of their machine as n goes to infinity, so their result is still in the limit, same as the typical laws of thermodynamics.

So this is primarily an interesting mathematical restatement at the quantum level. I don't know how useful this is, not having much knowledge about existing quantum information theory/thermodynamics.