2007 Fiscal Year Final Research Report Summary
Fractal Scaling of Area of Hysteresis Loop on Magnetic Inversion Experiment of Thin Metallic Films--the inductive nonequilibrium statistical mechanics based on time series analysis--
| Project/Area Number |
17540346
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Ibaraki University |
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Principal Investigator |
HASEGAWA Hiroshi Ibaraki University, College of Science, Associate Professor (70282283)
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| Project Period (FY) |
2005 – 2007
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| Keywords | nonequilibrium thermodynamics / nonequilibrium statistical mechanics / time series analysis / the second law of thermodynamics / bromate sulfite ferrocyanide reaction / Pareto law / self-organized criticality / superstatistics |
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| Research Abstract |
We have done several pioneer works on the inductive nonequilibrium statistical mechanics based on time series data. We have also made some progresses in foundation of nonequilibrium thermodynamics and statistical mechanics.
We applied the inductive nonequilibrium statistical mechanics to physical, chemical and economical data. Although our application to data of the magnetic inversion experiment of thin metallic films is still in the middle, we have done pioneer works in chemistry and economy, respectively.
In chemistry, we analyzed the oscillating pH data of Bromate-Sulfite-Ferrocyanide (BSF) chemical reaction using the particle filter. By extending the mathematical model proposed by Rabai-Kaminaga-Hanazaki we obtained quantitative agreement with experiment in the stationary and oscillatory states phase diagram [Ref. 2].
In economy, we reconsidered the size (sale or profit) distribution of business firms so called Parero distribution based on the stable eigen-functional. We derived a rigorous relation among Pareto index, logarithmic growth rates for both extended and contracting directions and flow rate. We confirmed it using the sales and profits data of Japanese business firms from 1983 to 2003 [Ref. 3].
We also made two progresses in foundation of nonequilibrium thermodynamics and statistical mec hanics. One is derivation of a fluctuation and dissipation type relation about thermodynamic work [Ref. 1]. The other is extension of the second law of thermodynamics to nonequilibrium intial distrib utions [Refs. 4 and 5].
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Research Products
(11 results)
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[Presentation] 企業サイズの統計力学2009
Author(s)
大滝由一, 小松宏文, 森田真倫, 長谷川博
Organizer
統計数理研究所研究会「経済物理とその周辺」
Place of Presentation
鳥取大学(鳥取市)
Year and Date
2009-01-24
Description
「研究成果報告書概要(和文)」より
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