Abstract
We consider how to describe Hamiltonian mechanics in generalized probabilistic theories with the states represented as quasiprobability distributions. We give general operational definitions of energy-related concepts. We define generalized 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 generalized energy eigenstates. This allows for a generalized 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. © 2024 American Physical Society.
| Original language | English |
|---|---|
| Article number | 120201 |
| Journal | Physical Review Letters |
| Volume | 132 |
| Issue number | 12 |
| Online published | 21 Mar 2024 |
| DOIs | |
| Publication status | Published - 22 Mar 2024 |
Funding
We are grateful to Andrew Garner and Dario Egloff for early discussions and to Meng Fei, Fil Simovic, Chelvanniththilan Sivapalan, and Ioannis Soranidis for feedback on the draft. L. J. and O. D. acknowledge support from the National Natural Science Foundation of China (Grants No. 12050410246, No. 1200509, No. 12050410245) and City University of Hong Kong (Project No. 9610623). The work of DRT was in part supported by the Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology.
Publisher's Copyright Statement
- COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: Jiang, L., Terno, D. R., & Dahlsten, O. (2024). Unification of Energy Concepts in Generalized Phase Space Theories. Physical Review Letters, 132(12), Article 120201. https://doi.org/10.1103/PhysRevLett.132.120201 The copyright of this article is owned by American Physical Society.