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Cited by 226Quantum Mechanics and ApplicationsQuantum chaos and dynamical systemsStatistical Mechanics and Entropy

The DOI matches its Crossref record; 61 of the 62 references it cites were found in a registry or an index.

Dynamical origin of quantum probabilities

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Valentini, Antony, Westman, Hans·2005·Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
DOI 10.1098/rspa.2004.1394
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Abstract

We study the origin of the Born probability rule ρ = | ψ | 2 in the de Broglie–Bohm pilot–wave formulation of quantum theory. It is argued that quantum probabilities arise dynamically, and have a status similar to thermal probabilities in ordinary statistical mechanics. This is illustrated by numerical simulations for a two–dimensional system. We show that a simple initial ensemble, with a non–standard distribution ρ ≠ | ψ | 2 of particle positions, evolves towards the quantum distribution to high accuracy. The relaxation process ρ →| ψ | 2 is quantified in terms of a coarse–grained H –function (equal to minus the relative entropy of ρ with respect to | ψ | 2 ), which is found to decrease approximately exponentially over time, with a time constant that accords with a simple theoretical estimate.

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Research works printed but not linked: 6

  1. Gleason A. M., 1957, J. Math. Mech., 6, 885
  2. Hardy L. 2002a Preprint quant-ph/0101012. · arXiv
  3. Valentini A. 2001 In Chance in physics: foundations and perspectives (ed. J. Bricmont et al .). Springer.
  4. Valentini A. 2004a Pilot-wave theory of physics and cosmology. Cambridge University Press. (In the press.)
  5. Valentini A., 2004, Phys. Lett. A. (In the press.)
  6. Wallace D. 2004 Stud. Hist. Phil. Mod. Phys. (In the press.)

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Metadata

Authors
Valentini, A., & Westman, H.
Affiliations
  • Augustus College, 14 Augustus Road, London SW19 6LN, UK
  • Chalmers University of Technology (SE)
Corresponding author
Valentini, Antony
ORCID
Valentini, Antony
Venue
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher
The Royal Society
Published
2005-01-08
Volume
461
Issue
2053
Pages
253-272
ISSN
  • 1364-5021 (ISSN-L)
  • 1471-2946
DOI
10.1098/rspa.2004.1394
OpenAlex
W2130195092
Cited by
226
References
62
Citations by year
2026: 3 · 2025: 8 · 2024: 4 · 2023: 14 · 2022: 10 · 2021: 11 · 2020: 12 · 2019: 36 · 2018: 9 · 2017: 7 · 2016: 8 · 2015: 12 · 2014: 10 · 2013: 4 · 2012: 18
FWCI
3.48
Type
journal article
Language
en
Open access
Licence
royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)
Locations
  • Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
Keywords
Born rule, Bohmian mechanics, quantum probability, H-function, Kullback-Leibler divergence, coarse-graining, two-dimensional quantum systems

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