Classical information geometry and its application to physics

Koki Tokeshi

Information geometry is a theory for statistical manifolds, on which many kinds of probability distributions are described geometrically. In particular, the so-called exponential family type probability distributions can be treated uniformly in the language of information geometry. The dually flat connection plays a crucial role in the theory as well as the Fisher information metric and Hessian structure of the manifolds. In this talk, I first review the general formulation of the theory. Although the theory has been succeeded to (re-)interpret the already known results in the statistical theory, its application to physics seems to be under construction, that is, many quantities have been calculated with their physical meanings remain uninterpreted, but some of them are referred to in this talk especially on the relation to general relativity or black hole physics.

[1] S. Amari, Information geometry and its applications, 2016.
[2] A. Fujiwara, Foundations of information geometry, 2015.
[3] H. Matsueda, Emergent GR from Fisher information metric, arXiv:1310.1831 [gr-qc].
[4] J. E. Aman and N. Pidokrajt, Critical phenomena and information geometry in black hole physics, arXiv:1001.2220 [gr-qc].
The first two are textbooks in English and Japanese respectively. The first person has extensively contributed to construct the theory while the second person studies quantum information geometry which is not referred to in this talk.

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Last-modified: 2020-11-27 (金) 14:46:56 (49d)