Deformed Algebras and Generalizations of Independence on Deformed Exponential Families

Autor: Hiroshi Matsuzoe, Tatsuaki Wada

Publikováno v: Entropy, Vol 17, Iss 8, Pp 5729-5751 (2015)

A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems. Tho

Externí odkaz: https://doaj.org/article/d430775b70f34385b80a21e2450b4155

Conjugate Representations and Characterizing Escort Expectations in Information Geometry

Autor: Tatsuaki Wada, Hiroshi Matsuzoe

Publikováno v: Entropy, Vol 19, Iss 7, p 309 (2017)

Based on the maximum entropy (MaxEnt) principle for a generalized entropy functional and the conjugate representations introduced by Zhang, we have reformulated the method of information geometry. For a set of conjugate representations, the associate

Externí odkaz: https://doaj.org/article/286972f1dd644d3896614eb366441a28

Advantages of q-logarithm representation over q-exponential representation from the sense of scale and shift on nonlinear systems

Autor: Antonio Maria Scarfone, Hiroki Suyari, Hiroshi Matsuzoe

Publikováno v: The European physical journal. Special topics (Online) 229 (2020): 773–785. doi:10.1140/epjst/e2020-900196-x
info:cnr-pdr/source/autori:Hiroki Suyari(1); Hiroshi Matsuzoe(2); and Antonio M. Scarfone(3)/titolo:Advantages of q-logarithm representation over q-exponential representation from the sense of scale and shift on nonlinear systems/doi:10.1140%2Fepjst%2Fe2020-900196-x/rivista:The European physical journal. Special topics (Online)/anno:2020/pagina_da:773/pagina_a:785/intervallo_pagine:773–785/volume:229

Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts with the d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::151cd4eb32954c5bac78690e4e793d31
https://doi.org/10.1140/epjst/e2020-900196-x

Invariant Metric Under Deformed Markov Embeddings with Overlapped Supports

Autor: Hiroshi Matsuzoe, Asuka Takatsu

Publikováno v: Results in Mathematics. 76

Due to Cencov’s theorem, there exists a unique family of invariant symmetric (0, 2)-tensor fields on the space of positive probability measures on a set of n-points indexed by $$n\in \mathbb {N}$$ under Markov embeddings. We deform Markov embedding

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ce11aadf8fad39f4774895ddc1e52173
https://doi.org/10.1007/s00025-021-01358-w

An eikonal equation approach to thermodynamics and the gradient flows in information geometry

Autor: Tatsuaki Wada, Hiroshi Matsuzoe, Antonio Maria Scarfone

Publikováno v: Physica. A
570 (2021): 1–15. doi:10.1016/j.physa.2021.125820
info:cnr-pdr/source/autori:Wada T.; Scarfone A.M.; Matsuzoe H./titolo:An eikonal equation approach to thermodynamics and the gradient flows in information geometry/doi:10.1016%2Fj.physa.2021.125820/rivista:Physica. A (Print)/anno:2021/pagina_da:1/pagina_a:15/intervallo_pagine:1–15/volume:570

We can incorporate a "time" evolution into thermodynamics as a Hamilton-Jacobi dynamics. A set of the equations of states in thermodynamics is considered as the generalized eikonal equation, which is equivalent to Hamilton-Jacobi equation. We relate

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::299dd9b753be12f6f1967f9934b0f268