Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T21:53:20.363328Z
Paper Citation Record · LEDGER
Phase space contraction rate for classical mixed states
As of 16 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2502.09361.
A citation records a reference. It does not transfer a finding from one paper to another.
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One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
45 of 45 outbound references displayed
- verified exact0
- verified fuzzy27
- unresolved18
- parse uncertain0
- malformed identifier0
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation c2fed547-4347-4e5c-a491-dc8db79c3c51 · outbound
This paper cites Since the density matrix is symmetric, we have the completeness relation Pd i=1 |δϕi⟩ ⟨δϕi| =.
Phase space contraction rate for classical mixed states Since the density matrix is symmetric, we have the completeness relation Pd i=1 |δϕi⟩ ⟨δϕi| =
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:22.175583Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6384d940-f7bf-4caa-b4d4-54741dbed9ab · outbound
This paper cites contraction rates.
Phase space contraction rate for classical mixed states contraction rates
Reference 2
- Resolution
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- raw_fallback, observed 2026-08-07T21:53:22.160757Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 648e770b-f6ba-4782-81f6-e9cee673a9d7 · outbound
This paper cites Zwanzig, Nonequilibrium Statistical Mechanics (Ox- ford University Press, New York, 2001).
Phase space contraction rate for classical mixed states Zwanzig, Nonequilibrium Statistical Mechanics (Ox- ford University Press, New York, 2001)
Reference 3
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- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:22.146334Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 924410c6-c867-4c25-874b-4eedc71fcba6 · outbound
This paper cites Aubin, Nonlinear analysis on manifolds.
Phase space contraction rate for classical mixed states Aubin, Nonlinear analysis on manifolds
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:22.131444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c17bc2eb-b4f8-4e2d-ad5b-f1e1622de6b3 · outbound
This paper cites Abraham, J.
Phase space contraction rate for classical mixed states Abraham, J
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:22.095965Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8644d240-3401-49ef-b637-cefc8d318955 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:22.048832Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 54a5707f-f1e3-4cbb-b11f-e13162b8aeb0 · outbound
This paper cites Gerlich, Die verallgemeinerte Liouville-Gleichung, Physica 69, 458 (1973).
Phase space contraction rate for classical mixed states Gerlich, Die verallgemeinerte Liouville-Gleichung, Physica 69, 458 (1973)
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:22.008911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dec090a8-724b-490a-860e-a9cee65737ee · outbound
This paper cites Prugovečki, Liouville dynamics for optimal stochastic phase-space representations of quantum mechanics, An- nals of Physics110, 102 (1978).
Phase space contraction rate for classical mixed states Prugovečki, Liouville dynamics for optimal stochastic phase-space representations of quantum mechanics, An- nals of Physics110, 102 (1978)
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.959551Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d772c23d-8360-45d3-a263-209049678e27 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.910947Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 901bc3d6-97fd-41aa-9e9b-96a6a519c2a3 · outbound
This paper cites Gaspard,Chaos, Scattering and Statistical Mechanics, Cambridge Nonlinear Science Series (Cambridge Univer- sity Press, Cambridge, 1998).
Phase space contraction rate for classical mixed states Gaspard,Chaos, Scattering and Statistical Mechanics, Cambridge Nonlinear Science Series (Cambridge Univer- sity Press, Cambridge, 1998)
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.792092Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 863b7870-c4b9-4464-b9a5-4f4bd5b2c2e3 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.706592Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dce0df93-5b80-47da-83e1-30a0132cc334 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.622814Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 34071c0d-5e4f-4328-8090-0488398d0b9f · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.570796Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3e3c583d-6685-4461-859b-c19f379a0363 · outbound
This paper cites Gaspard and G.
Phase space contraction rate for classical mixed states Gaspard and G
Reference 14
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- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.555475Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 531766b0-567a-406c-9794-52f45894c3ac · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.540558Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 98f8c56d-742a-4159-9a0d-24534bf11db0 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.526439Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4b7671ac-5dd1-442a-a120-2221ac68d83e · outbound
This paper cites Muir, A Treatise on the Theory of Determinants, editedbyW.H.Metzler(Longmans, GreenandCo.,Lon- don, 1933).
Phase space contraction rate for classical mixed states Muir, A Treatise on the Theory of Determinants, editedbyW.H.Metzler(Longmans, GreenandCo.,Lon- don, 1933)
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.512045Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f4ec335e-4ae7-4ab9-94ff-b6f085d09cad · outbound
This paper cites Andrey, The rate of entropy change in non- Hamiltonian systems, Phys.
Phase space contraction rate for classical mixed states Andrey, The rate of entropy change in non- Hamiltonian systems, Phys
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.497804Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 112da1bd-7091-4d4e-b401-f40c1c32637a · outbound
This paper cites therateofentropy change in non-Hamiltonian systems.
Phase space contraction rate for classical mixed states therateofentropy change in non-Hamiltonian systems
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.483093Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6b99d2cb-5d22-48fc-af87-1ad4d4525967 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.468509Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d1169372-573b-4b5a-9c87-680c92e710ac · outbound
This paper cites Betancourt, A general metric for Riemannian man- ifold Hamiltonian Monte Carlo, in International Con- ference on Geometric Science of Information(Springer,.
Phase space contraction rate for classical mixed states Betancourt, A general metric for Riemannian man- ifold Hamiltonian Monte Carlo, in International Con- ference on Geometric Science of Information(Springer,
Reference 21
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- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.432646Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 50029446-7950-4ec1-ac8c-e0599d3c4e09 · outbound
This paper cites Tuckerman, C.
Phase space contraction rate for classical mixed states Tuckerman, C
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.392624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 14bfe861-2cab-45a3-95c4-b846a30ee760 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:21.352456Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bcf481dd-4299-466c-9923-9f915f4dc0d1 · outbound
This paper cites Das and J.
Phase space contraction rate for classical mixed states Das and J
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.311402Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 98d3099b-239b-40ed-9070-84ecf3c36091 · outbound
This paper cites Das and J.
Phase space contraction rate for classical mixed states Das and J
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.218711Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dbe12a69-e476-4903-a2ea-e088eec119dc · outbound
This paper cites Das and J.
Phase space contraction rate for classical mixed states Das and J
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.105020Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 76c8c58c-6b08-4df6-a06a-bd4e6acf52bd · outbound
This paper cites Sahbani, S.
Phase space contraction rate for classical mixed states Sahbani, S
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:21.016789Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3e949c54-4a11-4e63-bd68-5b9a78eda107 · outbound
This paper cites Sergi, Non-Hamiltonian equilibrium statistical me- chanics, Phys.
Phase space contraction rate for classical mixed states Sergi, Non-Hamiltonian equilibrium statistical me- chanics, Phys
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:20.888405Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 46b96220-b64a-43a3-ba66-76140f68a99a · outbound
This paper cites Sergi and P.
Phase space contraction rate for classical mixed states Sergi and P
Reference 29
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- raw_fallback, observed 2026-08-07T21:53:20.850236Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ebd76e74-94f7-4fba-ad14-b394fc527938 · outbound
This paper cites Bravetti and D.
Phase space contraction rate for classical mixed states Bravetti and D
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:20.835120Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 904eb038-7d5a-418c-9756-e41ac955702c · outbound
This paper cites Pikovsky and A.
Phase space contraction rate for classical mixed states Pikovsky and A
Reference 31
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- raw_fallback, observed 2026-08-07T21:53:20.817563Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0ba425f3-f1b2-404e-9647-580269609100 · outbound
This paper cites A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators.
Phase space contraction rate for classical mixed states A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators
Reference 32
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- no resolver link, observed 2026-08-07T21:53:20.304157Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f3d649cf-fa95-487e-80e8-ac02bdde4ae9 · outbound
This paper cites Shankar,Principles of quantum mechanics(Springer Science & Business Media, 2012).
Phase space contraction rate for classical mixed states Shankar,Principles of quantum mechanics(Springer Science & Business Media, 2012)
Reference 33
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- no resolver link, observed 2026-08-07T21:53:20.309228Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2aaf3071-1b7f-46d7-8f18-431a0ad205cc · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T21:53:20.313468Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation df7e1cca-8f89-49c2-9250-ee0242704efb · outbound
This paper cites Das and J.
Phase space contraction rate for classical mixed states Das and J
Reference 35
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- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:20.783451Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f17e5580-f12a-43b9-a9c9-3b5d3bd4bcad · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:20.768325Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f8baceda-c448-4a6b-8613-98575981a561 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:20.753396Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9bdc36d1-7c21-4a74-8894-be1c6571ecd5 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:20.737377Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b6368432-798c-47c5-a24f-21aad390c3fc · outbound
This paper cites Goldstein, Classical Mechanics (Addison-Wesley, 1980).
Phase space contraction rate for classical mixed states Goldstein, Classical Mechanics (Addison-Wesley, 1980)
Reference 39
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T21:53:20.335577Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f64c1545-33bb-4d8a-9a71-f95f04657934 · outbound
This paper cites Benettin, L.
Phase space contraction rate for classical mixed states Benettin, L
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:20.696678Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 618bf413-f7f7-47e3-b69e-a65b776364c4 · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T21:53:20.657696Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d293272b-2150-495e-bcab-721f4c91713c · outbound
This paper cites an unresolved cited work.
Phase space contraction rate for classical mixed states Unresolved cited work
Reference 42
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T21:53:20.349716Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f98e1f4c-48c3-47f9-944c-e669bbf668ad · outbound
This paper cites Ruelle, Positivity of entropy production in nonequilib- rium statistical mechanics, J.
Phase space contraction rate for classical mixed states Ruelle, Positivity of entropy production in nonequilib- rium statistical mechanics, J
Reference 43
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- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:20.605634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f1877dfe-e1d9-4e26-8a90-54ef7801b838 · outbound
This paper cites Ruelle, Entropy production in nonequilibrium statis- tical mechanics, Commun.
Phase space contraction rate for classical mixed states Ruelle, Entropy production in nonequilibrium statis- tical mechanics, Commun
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:20.570382Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6495a6fa-0212-4790-b218-51a35e575e6f · outbound
This paper cites Klages,Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics (World Scientific, 2007).
Phase space contraction rate for classical mixed states Klages,Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics (World Scientific, 2007)
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T21:53:20.422066Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.