Unification of energy concepts in generalised phase space theories

Abstract

We consider how to describe Hamiltonian mechanics in generalised probabilistic theories with the states represented as quasi-probability distributions. We give general operational definitions of energy-related concepts. We define generalised energy eigenstates as the purest stationary states. Planck's constant plays two different roles in the framework: the phase space volume taken up by a pure state and a dynamical factor. The Hamiltonian is a linear combination of generalised energy eigenstates. This allows for a generalised Liouville time-evolution equation that applies to quantum and classical Hamiltonian mechanics and more. The approach enables a unification of quantum and classical energy concepts and a route to discussing energy in a wider set of theories.

5 pages and 2 pages of supplementary material. arXiv admin note: text overlap with arXiv:2403.00038

References in corpus (4)

• Higher-order interference and single-system postulates characterizing quantum theory
• Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
• Generalized dynamical theories in phase space and the hydrogen atom
• From reasonable postulates to generalised Hamiltonian systems

Cited by in corpus (4)

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