Unification of energy concepts in generalised phase space theories

• URL: http://arxiv.org/abs/2403.01398v1
• Date: Thu, 29 Feb 2024 09:04:13 GMT
• Title: Unification of energy concepts in generalised phase space theories
• Authors: Libo Jiang, Daniel R. Terno, and Oscar Dahlsten
• Abstract summary: We consider how to describe Hamiltonian mechanics in generalised probabilistic theories. We define generalised energy eigenstates as the purest stationary states. This allows for a generalised Liouville time-evolution equation that applies to quantum and classical Hamiltonian mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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