Are there dynamical physical systems that are governed by self-modifying Hamiltonians (Lagrangians), i.e. Hamiltonians (Lagrangians) determine not only the next point in phase space, but also the form of Hamiltonian (Lagrangian) in the next time step. Can concrete example of such system be provided.
I have heard that spin glasses can be used for modelling neural networks. Spin glasses are described by Hamiltonians. Maybe such self-modifying Hamiltonians can be used for describing self-modifying (evolving) neural networks with emergence of intelligence in them.