Skip to content
DraconiticResearch
Search Sources API
182,544 studies31 sourcesUpdated 45 min ago
PreprintarXiv licencearXiv

Understanding entropy using Aubin--Yau deformations

  • Tamás Darvas
  • Kewei Zhang
Open at sourcePDFDOICite

Abstract

In this paper we investigate three types of entropy that frequently appear in the research of Kähler geometry: the classical Kähler entropy, the radial entropy and the non-Archimedean entropy. We give a unifying interpretation for these entropies by showing that they can all be expressed as the derivative of the Monge--Ampère energy along certain Aubin--Yau type deformations. Such considerations also lead to a novel algebraic criterion for the existence of constant scalar curvature Kähler metrics.

Related

  1. Robustness of topological entropy under small area deformations
    Marcelo R. R. Alves, Matthias Meiwes, Beomjun Sohn
    arXivPreprintCC BY 4.0Full textDynamical systemsGeometry & topologyarXiv
  2. The Single Pole Battery: a Relativistic Understanding and Generalization of Clausius' Concept of Entropy
    Bert G. J. Frederiks
    OSF PreprintsPreprintCC BY 4.0Full textSystems & synthetic biologyEnvironmental science & pollutionOSF
  3. Aubin--Lions Compactness for Stieltjes--Bochner Evolution Graphs
    Francisco J. Fernández
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  4. Gaussian Normalized Coordinates and Risk-Neutral CDF Deformations
    Jian Sun
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  5. On deformations of foliated complex analytic structures II: Functors of Artin rings
    Chunghoon Kim
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{darvas2026understanding,
  title = {{Understanding entropy using Aubin--Yau deformations}},
  author = {Tamás Darvas and Kewei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21198},
  eprint = {2610.21198},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21198},
}
RIS
TY  - UNPB
TI  - Understanding entropy using Aubin--Yau deformations
AU  - Tamás Darvas
AU  - Kewei Zhang
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21198
UR  - https://arxiv.org/abs/2610.21198
AB  - In this paper we investigate three types of entropy that frequently appear in the research of Kähler geometry: the classical Kähler entropy, the radial entropy and the non-Archimedean entropy. We give a unifying interpretation for these entropies by showing that they can all be expressed as the derivative of the Monge--Ampère energy along certain Aubin--Yau type deformations. Such considerations also lead to a novel algebraic criterion for the existence of constant scalar curvature Kähler metrics.
ER  -