2001 Fiscal Year Final Research Report Summary
Tsallis entropy and nonextensive generalization of Boltzmann-Gibbs statistical mechanics
| Project/Area Number |
12640381
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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 |
物性一般(含基礎論)
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| Research Institution | University of Tsukuba (2001)
Nihon University (2000) |
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Principal Investigator |
ABE Sumiyoshi Institute of Physics, University of Tsukuba, 物理学系, 助教授 (70184215)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Tsallis statistics / nonadditive entropy / thermodynamic formalism / quantum entanglement / information theoretic uncertainty |
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| Research Abstract |
In 2000 and 2001, I have been addressing to the above research project from the viewpoints of thermodynamics and information theory. I have derived the most general composition law of entropy, which is compatible with the concept of "composability" and the zeroth law of thermodynamics. Starting with thus obtained nonadditive entropy, I have established the thermodynamic Legendre transform structure. This enables one to calculate thermodynamic properties of nonextensive systems. I have also studied the general properties of macroscopic thermodynamical equilibrium, and have found that such a state can be characterized not only by the standard Boltzmann factor but also by the Tsallis-type power-law factor. Then, nonadditive quantum information theory has been developed. I have found that this new theory has in some points superior to the ordinary additive von Neumann theory. Finally, I have discussed the information entropic uncertainty relation associated with the measurements of the position and momentum observables in the power-law wave packets, which may have the divergent variances. I could show that this information theoretic approach can reveal the properties of the wave packets, which cannot be discussed by using the standard Heisenberg-type formulation of the uncertainty relation.
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