Distribution-Metric Geometry: Phase Transitions as Information-Geometric Bifurcations
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| Format: | Recurso digital |
| Langue: | anglais |
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2025
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| _version_ | 1866901622074900480 |
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| author | delpech, maxime |
| author_facet | delpech, maxime |
| contents | <p> We introduce Distribution–Metric Geometry (DMG), a geometric framework for analyz<br>ing phase transitions directly in the space of empirical probability distributions generated<br> by microscopic models. Instead of focusing on model-specific order parameters, DMG con<br>structs a multi-metric embedding of each model into an information-geometric manifold.<br> Phase transitions then appear as geometric events: sudden reorientation of the trajectory in<br> metric space, peaks in geometric speed and curvature, and temporary expansion of intrinsic<br> dimensionality. Across three classical 2D lattice models (Villain, XY, Ising), DMG reveals<br> that their trajectories in metric space require, respectively, one, two, and three principal ge<br>ometric modes. These intrinsic dimensions are stable under the choice of metrics and system<br> size, and behave as robust geometric invariants of each model. . The framework is model<br>agnostic and extends naturally to complex systems where traditional order parameters are<br> unknown or purely topological.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17778979 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Distribution-Metric Geometry: Phase Transitions as Information-Geometric Bifurcations delpech, maxime Information Geometry Phase Transitions Statistical Mechanics Geometric Representation of Phases Fisher Information Critical Phenomena Optimal Transport Wasserstein Distance Condensed matter physics Statistical mechanics Information Theory Machine learning Kernel Methods Renormalization Complex Systems <p> We introduce Distribution–Metric Geometry (DMG), a geometric framework for analyz<br>ing phase transitions directly in the space of empirical probability distributions generated<br> by microscopic models. Instead of focusing on model-specific order parameters, DMG con<br>structs a multi-metric embedding of each model into an information-geometric manifold.<br> Phase transitions then appear as geometric events: sudden reorientation of the trajectory in<br> metric space, peaks in geometric speed and curvature, and temporary expansion of intrinsic<br> dimensionality. Across three classical 2D lattice models (Villain, XY, Ising), DMG reveals<br> that their trajectories in metric space require, respectively, one, two, and three principal ge<br>ometric modes. These intrinsic dimensions are stable under the choice of metrics and system<br> size, and behave as robust geometric invariants of each model. . The framework is model<br>agnostic and extends naturally to complex systems where traditional order parameters are<br> unknown or purely topological.</p> |
| title | Distribution-Metric Geometry: Phase Transitions as Information-Geometric Bifurcations |
| topic | Information Geometry Phase Transitions Statistical Mechanics Geometric Representation of Phases Fisher Information Critical Phenomena Optimal Transport Wasserstein Distance Condensed matter physics Statistical mechanics Information Theory Machine learning Kernel Methods Renormalization Complex Systems |
| url | https://doi.org/10.5281/zenodo.17778979 |