Persistent Entropy as a Detector of Phase Transitions
Quick summary
arXiv:2602.09058v2 Announce Type: replace-cross Abstract: Persistent entropy is a scalar summary of persistence barcodes widely used to detect regime changes, yet there is no account of when a structural change in a barcode must produce a detectable change in entropy. We establish a model-agnostic theorem supplying such conditions. Treating persistence diagrams as random objects indexed by a control parameter, we identify a dispersion-condensation mechanism in the normalized persistence weights and derive an explicit lower bound on the entropy difference between the two regimes, valid with hig
Key takeaways
- arXiv:2602.09058v2 Announce Type: replace-cross Abstract: Persistent entropy is a scalar summary of persistence barcodes widely used to detect regime changes, yet there is no account of when a structural change in a barcode must produce a detectable change in entropy.
- We establish a model-agnostic theorem supplying such conditions.
- Treating persistence diagrams as random objects indexed by a control parameter, we identify a dispersion-condensation mechanism in the normalized persistence weights and derive an explicit lower bound on the entropy difference between the two regimes, valid with hig
Why it matters
This model development creates a new option for users and a new testing obligation for developers. A fixed evaluation set comparing quality, cost and failure behavior is more useful than launch claims.
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