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arXiv · 2403.01398

Unification of energy concepts in generalised phase space theories

Libo Jiang·Daniel R. Terno·Oscar Dahlsten
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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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Libo Jiang, Daniel R. Terno, Oscar Dahlsten. 2024-02-29. Unification of energy concepts in generalised phase space theories. https://doi.org/10.1103/physrevlett.132.120201

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