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Record W2095752422 · doi:10.1142/s0219525905000373

EXTENDED ENTROPIES AND DISORDER

2005· article· en· W2095752422 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueAdvances in Complex Systems · 2005
Typearticle
Languageen
FieldPhysics and Astronomy
TopicStatistical Mechanics and Entropy
Canadian institutionsWestern University
FundersNatural Sciences and Engineering Research Council of CanadaSchweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
KeywordsMathematicsConjectureEntropy (arrow of time)SketchTsallis entropyStatistical physicsRényi entropyPure mathematicsPrinciple of maximum entropyStatisticsPhysicsQuantum mechanicsAlgorithmTsallis statistics

Abstract

fetched live from OpenAlex

Landsberg's notion of disorder, entropy normalized to maximum entropy, was originally proposed for the Shannon information-theoretic entropy to overcome extensivity-based deficiencies of entropy as a measure of disorder. We generalize Landsberg's concept to three classes of extended entropies: Rényi, Tsallis and Landsberg–Vedral. We show an intimate connection between the Rényi disorders and the spectrum of dimensions known as multifractals. Three examples are treated, including one for power law distributions and one based on the logistic map. On the basis of the three examples, it is demonstrated that all three classes of extended disorder are required to fully characterize the corresponding properties of a system. We conjecture, and sketch a proof to support, that all three extended disorders are also sufficient to completely determine a dimension spectrum.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.914
Threshold uncertainty score0.318

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.010
GPT teacher head0.280
Teacher spread0.269 · 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