Classical Mechanics versus Thermodynamics (Part 4)

Thanks to the precise mathematical analogy between classical mechanics and thermodynamics that we saw last time, we can define Poisson brackets in thermodynamics just as in classical mechanics. That is, we can define Poisson brackets of quantities like entropy, temperature, volume and pressure. But what does this mean?

Furthermore, we can get quantum mechanics from classical mechanics by replacing Poisson brackets by commutators. That’s a brief summary of a long story, but by now this story ...