What question did this study set out to answer?

The research aims to establish a unified geometric framework that connects transition phenomena in thermodynamics, statistical learning, and information theory.

March 10, 2026Open Access

Informational Transitions: A Unified Geometric Framework Across Thermodynamics, Learning, and Information

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LVLuc de Veigy

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Implication

Proposes a geometric framework linking transitions across thermodynamics, learning, and information, suggesting a unified mathematical structure.

Key Points

The research aims to establish a unified geometric framework that connects transition phenomena in thermodynamics, statistical learning, and information theory.
Proposed a one-parameter family of variational functionals to describe transitions.
Developed a value function based on the infimum of the variational functionals.
Analyzed the transitions through changes in the exposed face of the lower convex hull of the attainable set.
Introduced rupture operators to realize transitions geometrically.
Identified first-order transitions with non-differentiable points in the value function.
Described second-order transitions through continuous evolution of minimizers with changing stability.
Demonstrated common variational mechanisms relevant to classical constructions across fields.
Illustrated geometric insights using a minimal numerical example.

Cite This Study

Luc de Veigy (2026) studied this question.

synapsesocial.com/papers/69af950a70916d39fea4c3bc https://doi.org/10.5281/zenodo.18913283

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Implication

Proposes a geometric framework linking transitions across thermodynamics, learning, and information, suggesting a unified mathematical structure.

Informational Transitions: A Unified Geometric Framework Across Thermodynamics, Learning, and Information

Discussion

Member takes

Implication

Key Points

Cite This Study

Informational Transitions: A Unified Geometric Framework Across Thermodynamics, Learning, and Information

Discussion

Member takes

Implication

Key Points

Cite This Study

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