Why I do not believe that heat is mechanical movement. My first objection is, that I do not believe randomness to be reducable to classical movement.
Classical movement is deterministic.
Suppose that I toss a fair coin a hunderd times, and that we repeat this process a great many times. We then see the laws of probability emerge. In order to reduce the observed statistical distributions to classical mechanics, I have to follow the history of each of my many tosses into the past. Each H will be the result of a previous configuration that already contained the certainty of the outcome of the toss being H. Suppose that we follow the history of each toss for , say, one day into the past. With other words, we again found the same statistical distribution that popped up in the tosses.