I read quickly your article, and it is interesting.
I am thinking that if it is possible to have a bijection between each statistical system and a thermodynamic system (for example the blind child and a thermodynamic process), then it is possible to associate to each statistical system some physical quantity, and it is possible to apply the law of thermodynamic.
So, if there are two boxes, with red balls (hot molecules) and white balls (cold molecules), and a blind child (no physical measure) that make a random choice for each time step, then asymptotically the system is in equilibrium; if we write the second law of thermodynamics (in equilibrium point) for the blind child, then we must write that is impossible the passing of N red balls (for example 20) from a boxe to an other boxes (Clausius say that the entropy fluctutations are impossible).
I can understand the impossibility of the perpetual motion: it is impossible the infinite reproduction of the same sequence of extractions from the two boxes, but I think that the Clausius statement is so weak.