| 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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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,730,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
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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 / カオス / 混合性 / ボルツマン分布 / 熱力学エントロピー / フラクタル・スケーリング / シャノン・エントロピー / 量子Entanglement / 量子カオス / 長時間相関 / ヒステリス・ループ / 磁気反転実験 / excess heat production / fluctuation-dissipation theorem / thermodynamic entropy / Barkhausen jump / magnetic reversalexperimnt / entanglement / self organized criticality |
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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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