Unification of energy concepts in generalised phase space theories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917624581980160 |
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| author | Jiang, Libo Terno, Daniel R. Dahlsten, Oscar |
| author_facet | Jiang, Libo Terno, Daniel R. Dahlsten, Oscar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unification of energy concepts in generalised phase space theories Jiang, Libo Terno, Daniel R. Dahlsten, Oscar Quantum Physics Classical Physics 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. |
| title | Unification of energy concepts in generalised phase space theories |
| topic | Quantum Physics Classical Physics |
| url | https://arxiv.org/abs/2403.01398 |