On defining the Hamiltonian beyond quantum theory

An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.

Foundations of Physics 48, 982 (2018)

D. Branford, O. Dahlsten, A. Garner

On defining the Hamiltonian beyond quantum theory

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories—a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories.

More in Information thermodynamics

  • Proceedings of the Royal Society A

    Quantum thermodynamics

    Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.

  • Physical Review Letters

    Photonic Maxwell's demon

    With inspiration from Maxwell’s classic thought experiment, it is possible to extract macroscopic work from microscopic measurements of photons.

  • New Journal of Physics

    Worst-case work entropic equality

    A new equality which depends on the maximum entropy describes the worst-case amount of work done by finite-dimensional quantum systems.

  • New Journal of Physics

    A measure of majorization

    Single-shot information theory inspires a new formulation of statistical mechanics which measures the optimal guaranteed work of a system.