Wow, it looks extremely interesting! You know, it's bizarre, I recently pursued a similar approach, attempting to derive quadratic kinetic energy of an automat

Wow, it looks extremely interesting! You know, it's bizarre, I recently pursued a similar approach, attempting to derive quadratic kinetic energy of an automaton controlled by a computer program (it used a circular tape to decide whether to move left or right). I set up a coarse-groaning, identifying energy with information, well, negentropy of the state of the tape, and arrived at similar results: higher energy = fewer microstates, in other words, there are fewer programs that move at the speed of light than at some slower speed. Which makes sense! There is only one tape that tells the automaton to move right at every step. Toffoli says exactly this: "A low-energy state is 'cheap' because it is 'common', there are so many ways to achieve it". Conservation of energy is exactly microscopic reversibility! What could be cleaner? That whole approach is on the shelf for now, because I first want to develop a discrete version of contact, and thence symplectic geometry, since that will provide the mathematical formalism to express a kind of "discrete classical physics", rather than just a single toy model. Anyway, I'm beyond grateful for this reference!