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Record W2063955268 · doi:10.1063/1.533334

Return to equilibrium

2000· article· en· W2063955268 on OpenAlexaff
Volker Bach, Jürg Fröhlich, Israel Michael Sigal

Bibliographic record

VenueJournal of Mathematical Physics · 2000
Typearticle
Languageen
FieldMathematics
TopicSpectral Theory in Mathematical Physics
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsOperator (biology)Black-body radiationMassless particleThermodynamic equilibriumHamiltonian (control theory)PhysicsThermal equilibriumQuantum mechanicsPhotonAtom (system on chip)Mathematical physicsRadiationMathematicsChemistry

Abstract

fetched live from OpenAlex

We study an atom with finitely many energy levels in contact with a heat bath consisting of photons (blackbody radiation) at a temperature T>0. The dynamics of this system is described by a Liouville operator, or thermal Hamiltonian, which is the sum of an atomic Liouville operator, of a Liouville operator describing the dynamics of a free, massless Bose field, and a local operator describing the interactions between the atom and the heat bath. We show that an arbitrary initial state that is normal with respect to the equilibrium state of the uncoupled system at temperature T converges to an equilibrium state of the coupled system at the same temperature, as time tends to +∞ (return to equilibrium).

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)0.000
metaresearch head score (Gemma)0.003
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: Empirical
Teacher disagreement score0.008
Threshold uncertainty score0.027

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0010.002
Scholarly communication0.0010.002
Open science0.0010.002
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0080.001

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 head0.047
GPT teacher head0.334
Teacher spread0.288 · 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

Citations166
Published2000
Admission routes1
Has abstractyes

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