I strongly disagree. "physical things" are precisely "observational quantities" and entropy is just as real as temperature/pressure or whatever thermodynamical quantity.

Going back to OP's question. The only physical law that differentiates past from future is entropy, all other (fundamental) physical laws are time reversal invariants. Many people believe that the passing of time is how we experience a gradient of entropy (Hawking has a beautiful argument of why the only way we can remember something is by increasing entropy in his brief history of time, I can find the exact part if you are interested). From this perspective, it is not that it just so happens that entropy increases with time, it is that we can only remember stuff with less entropy and the stuff we remember is what we call the past.