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.
- L. Hardy, arXiv preprint quant-ph/0101012 (2001).
- J. Barrett, Physical Review A 75, 032304 (2007).
- P. Janotta and H. Hinrichsen, Journal of Physics A: Mathematical and Theoretical 47, 323001 (2014).
- D. R. Terno, arXiv preprint arXiv:2309.05014 (2023).
- H. Barnum, M. P. Müller, and C. Ududec, New Journal of Physics 16, 123029 (2014).
- Y. L. Lin and O. C. Dahlsten, Physical Review A 102, 062210 (2020).
- D. Branford, O. C. O. Dahlsten, and A. J. P. Garner, Foundations of Physics 48, 982 (2018).
- M. Plávala and M. Kleinmann, Phys. Rev. Lett. 128, 040405 (2022a).
- M. Plávala and M. Kleinmann, arXiv preprint arXiv:2212.12267 (2022b).
- L. Jiang, O. Dahlsten, and D. Terno, In progress (2024).
- V. I. Arnold, Mathematical methods of classical mechanics, Vol. 60 (Springer Science & Business Media, 2013).
- H. W. Lee, Physics Reports-Review Section of Physics Letters 259, 147 (1995).
- E. Wigner, Physical Review 40, 749 (1932).
- A. Royer, Phys. Rev. A 15, 449 (1977).
- T. Hakioglu and E. Tepedelenlioglu, Journal of Physics A: Mathematical and General 33, 6357 (2000).
- M. P. Müller and C. Ududec, Phys. Rev. Lett. 108, 130401 (2012).
- O. C. O. Dahlsten, A. J. P. Garner, and V. Vedral, Nature Communications 5, 4592 (2014).
- H. Barnum and A. Wilce, Electronic Notes in Theoretical Computer Science 270, 3 (2011).
- S. D. Bartlett, T. Rudolph, and R. W. Spekkens, Phys. Rev. A 86, 012103 (2012).
- N. T. Zung, Arch. Rational Mech. Anal. 229, 789–833 (2018).
- J. Smith, Journal of Algebra 456, 46 (2016).
- A. Peres, Quantum theory: concepts and methods (Kluwer, Dordrecht, 1995).
- S. E. Venegas-Andraca, Quantum Information Processing 11, 1015 (2012).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.