Classical mechanics as the high-entropy limit of quantum mechanics

          @misc{ scivideos_PIRSA:25100174,
            doi = {10.48660/25100174},
            url = {https://pirsa.org/25100174},
            author = {Carcassi, Gabriele},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Classical mechanics as the high-entropy limit of quantum mechanics},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100174 see, \url{https://scivideos.org/pirsa/25100174}}
          }
          

Abstract

We show that classical mechanics can be recovered as the high-entropy limit of quantum mechanics. The mathematical limit $\hbar \to 0$ can be recovered by decreasing entropy of pure states to minus infinity, in the same way that non-relativistic mechanics can be recovered mathematically by increasing the speed of light c to plus infinty. Physically, these limits are more appropriately understood as a high entropy limit and low speed limit respectively, representing approximations that are independent of underlying mechanism. With this approach, the classical limit is both formally and conceptually similar to the non-relativistic limit, and is independent of interpretation. It also gives an intuitive understanding to the Dirac correspondence principle: it is looking for a theory with lower entropy bound that, at high entropy, recovers classical mechanics. Given that the Moyal bracket is the unique one-parameter Lie-algebraic deformation of the Poisson bracket, quantum mechanics is the only theory that can provide such a lower bound on the entropy.