Displacement convexity of Boltzmann's entropy characterizes the strong\n energy condition from general relativity
Bibliographic record
Abstract
On a Riemannian manifold, lower Ricci curvature bounds are known to be\ncharacterized by geodesic convexity properties of various entropies with\nrespect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal\ntransportation. These notions also make sense in a (nonsmooth) metric measure\nsetting, where they have found powerful applications. This article initiates\nthe development of an analogous theory for lower Ricci curvature bounds in\ntimelike directions on a (globally hyperbolic) Lorentzian manifold. In\nparticular, we lift fractional powers of the Lorentz distance (a.k.a. time\nseparation function) to probability measures on spacetime, and show the strong\nenergy condition of Hawking and Penrose is equivalent to geodesic convexity of\nthe Boltzmann-Shannon entropy there. This represents a significant first step\ntowards a formulation of the strong energy condition and exploration of its\nconsequences in nonsmooth spacetimes, and hints at new connections linking the\ntheory of gravity to the second law of thermodynamics.\n
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
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".