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

被引：9

作者：

Wada, Tatsuaki ^{[1
]}

Scarfone, Antonio M. ^{[2
]}

Matsuzoe, Hiroshi ^{[3
]}

机构：

[1] Ibaraki Univ, Reg Elect & Elect Syst Engn, Nakanarusawa Cho, Hitachi, Ibaraki 3168511, Japan

[2] Politecn Torino, Consiglio Nazl Ric ISC CNR, Ist Sistemi Complessi, I-10129 Turin, Italy

[3] Nagoya Inst Technol, Dept Comp Sci & Engn, Showa Ku, Gokiso Cho, Nagoya, Aichi 4668555, Japan

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2021年 / 570卷

基金：

日本学术振兴会;

关键词：

Eikonal equation; Gradient-flow equations; Information geometry; Hamilton-Jacobi dynamics; Thermodynamics; Vielbein; FORMALISM;

D O I：

10.1016/j.physa.2021.125820

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We can incorporate a "time'' evolution into thermodynamics as a Hamilton-Jacobi dynamics. A set of the equations of state in thermodynamics is considered as the generalized eikonal equation, which is equivalent to Hamilton-Jacobi equation. We relate the Hamilton-Jacobi dynamics of a simple thermodynamic system to the gradient flows in information geometry. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：15

共 26 条

[1]

Amari SI, 2016, APPL MATH SCI, V194, P1, DOI 10.1007/978-4-431-55978-8

[2] A Hamiltonian approach to Thermodynamics [J].

Baldiotti, M. C. ;

Fresneda, R. ;

Molina, C. .

ANNALS OF PHYSICS, 2016, 373 :245-256

[3]

Blau M, 2012, LECT NOTES GEN RELAT

[4]

Boumuki N., 2016, Fund. J. Math. Math. Sci, V6, P51

[5] Measuring thermodynamic length [J].

Crooks, Gavin E. .

PHYSICAL REVIEW LETTERS, 2007, 99 (10)

[6]

Dirac PAM., 1996, GEN THEORY RELATIVIT, DOI [10.1515/9781400884193, DOI 10.1515/9781400884193]

[7]

Einstein A, 1928, SITZBER PREUSS AKAD, P217

[8] GRADIENT SYSTEMS IN VIEW OF INFORMATION GEOMETRY [J].

FUJIWARA, A ;

AMARI, SI .

PHYSICA D, 1995, 80 (03) :317-327

[9]

Fujiwara A., 1993, RIMS KOKYUROKU, V822, P32

[10] Contact geometry and thermodynamics of black holes in AdS spacetimes [J].

Ghosh, Aritra ;

Bhamidipati, Chandrasekhar .

PHYSICAL REVIEW D, 2019, 100 (12)

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