Statistical mechanics and the ontological interpretation
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In pilot-wave theory, a mixed quantum state is described by a preferred decomposition of ρ into a statistical mixture of ontological pilot waves Ψ_α.
“In pilot-wave theory, a mixed quantum state is described by a preferred decomposition of ˆ ρ into a statistical mixture (with weights p α ) of ontological pilot waves Ψ α (Bohm and Hiley 1996).”
From De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial? (2008) · cites this paper as Bohm and Hiley 1996
Cites
PRINCIPLES OF STATISTICAL MECHANICS
Rogalski, M. S., & Palmer, S. B. (2014) · CRC Press eBooks · doi:10.1201/b16000-30 · Cited by 1,203 · see citing works
On the interpretation of measurement in quantum theory
Zeh, H. D. (1970) · Foundations of Physics · doi:10.1007/bf00708656 · Cited by 1,028 · see citing works
Equilibrium and Nonequilibrium Statistical Mechanics
Jones, M. C. (1975) · Physics Bulletin · doi:10.1088/0031-9112/26/12/042 · Cited by 998 · see citing works
Equilibrium and Non-equilibrium Statistical Mechanics
Balescu, R., & Kaufman, A. N. (1976) · Physics Today · doi:10.1063/1.3024522 · Cited by 518 · see citing works
An ontological basis for the quantum theory
Böhm, D., Hiley, B. J., & Kaloyerou, P. N. (1987) · Physics Reports · doi:10.1016/0370-1573(87)90024-x · Cited by 443 · see citing works
Self-citationPrinciples of Statistical Mechanics
Girifalco, L. A. (2000) · doi:10.1093/oso/9780195119657.003.0002 · Cited by 57 · see citing works
Rogalski, M. S., & Palmer, S. B. (2014) · CRC Press eBooks · doi:10.1201/b16000-31 · Cited by 8 · see citing works
Flagged first, then by citations
2 of the 9 references couldn’t be matched to a known paper.
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De Broglie–Bohm Pilot‐Wave Theory: Many Worlds in Denial?
Valentini, A. (2010) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199560561.003.0019 · Cited by 60 · see citing works
The density matrix in the de Broglie-Bohm approach
Maroney, O. J. E. (2003) · CERN Document Server (European Organization for Nuclear Research) · Cited by 22 · see citing works
Is - kTr(ρlnρ) the Entropy in Quantum Mechanics
Shenker, O. R. (1999) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/50.1.33 · Cited by 20 · see citing works
Information and Entropy in Quantum TheoryPreprint
Maroney, O. J. E. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0411172 · Cited by 20 · see citing works
The Density Matrix in the de Broglie--Bohm Approach
Maroney, O. J. E. (2005) · Foundations of Physics · doi:10.1007/s10701-004-1985-7 · Cited by 14 · see citing works
Quantum statistical mechanics from a Bohmian perspective
Nikolić, H. (2024) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2024.129757 · Cited by 2 · see citing works
Causality, Nonlocality, and Entanglement in Quantum Mechanics
de la Peña, L., Cetto, A. M., & Hernández, A. V. (2014) · Springer eBooks · doi:10.1007/978-3-319-07893-9_8 · Cited by 1 · see citing works
Non-Markovian quantum Brownian motion: a non-Hamiltonian approachPreprint
Bolivar, A. O. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1503.07951 · Cited by 1 · see citing works
De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?
Valentini, A. (2008) · arXiv · doi:10.48550/arxiv.0811.0810
“l. 1998; Zurek 2003, pp. 745{47).14 In pilot-wave theory, a mixed quantum state is described by a preferred decomposition of ^ˆinto a statistical mixture (with weights p ) of ontological pilot waves (Bohm and Hiley 1996). For a given element of the ensemble, the de Broglian velocity of the conguration is determined by…”
BackgroundThe partition function in the quantum-to-classical transition
Cui, B. (2025) · Physics Letters A · doi:10.1016/j.physleta.2025.131185
On the foundations and interpretations of Bohm’s approach to quantum mechanics
Orozco, J. A. M. (2013) · Utrecht University Repository (Utrecht University)
- Authors
- Bohm, D., & Hiley, B. J.
- Affiliations
- University of London (GB)
- ORCID
- Hiley, B. J.
- Venue
- Foundations of Physics
- Published
- 1996-06
- Volume
- 26
- Issue
- 6
- Pages
- 823-846
- ISSN
- 0015-9018 (ISSN-L)
- 1572-9516
- OpenAlex
- W2010376390
- Cited by
- 11
- References
- 9
- Citations by year
- 2025: 1 · 2024: 1 · 2015: 1 · 2014: 1 · 2013: 1
- FWCI
- 0.24
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Foundations of Physics (publishedVersion)
- 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 › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- ontological interpretation of quantum mechanics, quantum statistical mechanics, wave functions, density matrix, wave function of the universe, non-equilibrium thermodynamics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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