Convergence

The Only Rule in the Room

An equation discovered for hot gases turns out to be the only one that respects strangers.

One axiom, four domains, the same equation

Hover a spoke to see why each field arrives at Boltzmann/logit.

independent fields

The same exponential rule governs gas molecules, shoppers, pedestrians, and emotional decisions. Not by coincidence — by uniqueness theorem.

Sources: arXiv 2307.11372 (2023), Caltech (2024), IJTE (2019), Psych Science 27(6) and the Kahneman line. Spoke geometry is illustrative; metrics shown are the headline figure each field publishes.

PHYSICS

Boltzmann distribution is the only law for uncoupled systems.

arXiv paper proves Boltzmann distribution is unique family satisfying independence for uncoupled systems.

Caltech proof shows Boltzmann as sole law accurately describing unrelated systems in physics.

Mathematical characterization via endomorphisms of convolution semigroup confirms uniqueness.

correlates

ECONOMICS

Boltzmann distribution is the only law for uncoupled systems.

Caltech economists proved Boltzmann distribution is sole model maintaining independence in unrelated systems, ruling out alternatives.

Multinomial logit model derives from Gibbs-Boltzmann, predicts independent choices via IIA property in choice sets.

1999 paper derives multinomial logit as bounded rational choice model, matching Gibbs-Boltzmann in statistical physics.

correlates

URBAN PLANNING

94.9%

Logit model correctly classified 94.9% of pedestrian gap acceptance cases.

Pedestrian gap acceptance logit model achieved neglected R Square of 0.882.

Area under ROC curve for pedestrian gap acceptance logit models was 0.98.

Variables VSC, PDV, PA, Vp significantly impacted pedestrian gap acceptance in logit models.

correlates

PSYCHOLOGY

27(6)

Psych Science issue with affective decision models using logit-like choice prediction.

Kahneman (2003) proved dominance of irrational emotional decisions over rational ones in behavior.

Tversky and Kahneman experiments (1979, 1984) showed task framing as gain or loss drives choice direction.

Paulus et al. (2005a,b) found negative emotions reduce search time and info use in choices.

PHYSICS

Boltzmann distribution is the only law for uncoupled systems.

arXiv paper proves Boltzmann distribution is unique family satisfying independence for uncoupled systems.

Caltech proof shows Boltzmann as sole law accurately describing unrelated systems in physics.

Mathematical characterization via endomorphisms of convolution semigroup confirms uniqueness.

correlates

ECONOMICS

Boltzmann distribution is the only law for uncoupled systems.

Caltech economists proved Boltzmann distribution is sole model maintaining independence in unrelated systems, ruling out alternatives.

Multinomial logit model derives from Gibbs-Boltzmann, predicts independent choices via IIA property in choice sets.

1999 paper derives multinomial logit as bounded rational choice model, matching Gibbs-Boltzmann in statistical physics.

correlates

URBAN PLANNING

94.9%

Logit model correctly classified 94.9% of pedestrian gap acceptance cases.

Pedestrian gap acceptance logit model achieved neglected R Square of 0.882.

Area under ROC curve for pedestrian gap acceptance logit models was 0.98.

Variables VSC, PDV, PA, Vp significantly impacted pedestrian gap acceptance in logit models.

correlates

PSYCHOLOGY

27(6)

Psych Science issue with affective decision models using logit-like choice prediction.

Kahneman (2003) proved dominance of irrational emotional decisions over rational ones in behavior.

Tversky and Kahneman experiments (1979, 1984) showed task framing as gain or loss drives choice direction.

Paulus et al. (2005a,b) found negative emotions reduce search time and info use in choices.

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