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Record W2963345940 · doi:10.4153/cmb-2011-121-9

An Optimal Transport View of Schrödinger's Equation

2012· article· en· W2963345940 on OpenAlexvenueno aff
Max‐K. von Renesse

Bibliographic record

VenueCanadian Mathematical Bulletin · 2012
Typearticle
Languageen
FieldMathematics
TopicGeometric Analysis and Curvature Flows
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsSymplectic geometryWasserstein metricProbability measureLift (data mining)Symplectic manifoldSpace (punctuation)Pure mathematicsMathematical analysis

Abstract

fetched live from OpenAlex

Abstract We show that the Schrödinger equation is a lift of Newton's third law of motion on the space of probability measures, where derivatives are taken with respect to the Wasserstein Riemannian metric. Here the potentialμ→F(μ) is the sum of the total classical potential energy (V, μ) of the extended system and its Fisher information . The precise relation is established via a well-known (Madelung) transform which is shown to be a symplectic submersion of the standard symplectic structure of complex valued functions into the canonical symplectic space over the Wasserstein space. All computations are conducted in the framework of Otto's formal Riemannian calculus for optimal transportation of probability measures.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.005
Threshold uncertainty score0.016

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0010.000
Science and technology studies0.0010.002
Scholarly communication0.0010.003
Open science0.0010.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0050.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.044
GPT teacher head0.279
Teacher spread0.236 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations43
Published2012
Admission routes1
Has abstractyes

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