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On counterexamples to the unification of free entropy

  • David Jekel
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Abstract

It has been a long-standing open problem to determine when two versions of Voiculescu's free entropy, χ and χ*, agree. OpenAI recently generated the first example with −∞ < χ< χ*. We give a detailed presentation of a similar example, and explicitly show the separation between free Fisher information and the large-n limit of classical Fisher information through the relationship with Wasserstein distance. We thus situate the example in the context of probability theory and information geometry.

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Cite

BibTeXRIS
BibTeX
@misc{jekel2026counterexamples,
  title = {{On counterexamples to the unification of free entropy}},
  author = {David Jekel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27243},
  eprint = {2610.27243},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27243},
}
RIS
TY  - UNPB
TI  - On counterexamples to the unification of free entropy
AU  - David Jekel
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27243
UR  - https://arxiv.org/abs/2610.27243
AB  - It has been a long-standing open problem to determine when two versions of Voiculescu's free entropy, χ and χ^*, agree. OpenAI recently generated the first example with −∞ < χ< χ^*. We give a detailed presentation of a similar example, and explicitly show the separation between free Fisher information and the large-n limit of classical Fisher information through the relationship with Wasserstein distance. We thus situate the example in the context of probability theory and information geometry.
ER  -