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Nonextensive Statistical Mechanics and Its Applications : Lecture Notes in Physics - Sumiyoshi Abe

Nonextensive Statistical Mechanics and Its Applications

Lecture Notes in Physics

By: Sumiyoshi Abe (Editor), Yuko Okamoto (Editor)

Hardcover Published: January 2001
ISBN: 9783540412083
Number Of Pages: 278

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from the content: PartI: Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status.- Quantum Density Matrix Description of Nonextensive Systems.- Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations.- Computational Methods for the Simulation of Classical and Quantum Manybody Systems Sprung from the Nonextensive Thermostatistics.- Part II: Correlation Induced by Nonextensivity and the Zeroth Law of Thermodynamics.- Dynamic and Thermodynamic Stability of Nonextensive Systems.- Generalized Simulated Annealing Algorithms Using Tsallis Statistics: Application to Spin Glass Model.- Protein Folding Simulations by a Generalize-Ensemble Algorithm Based on Tsallis Statistics.

"This is an extremely interesting book that consists of a set of articles based on the generalization of entropic measure introduced be C. Tsallis. [...] Topics examined in the book cover a wide variety of interesting material such as classical and quantum many body systems, thermodynamic systems, applications to spin glass models and to protein folding. All of these can be read even by the non-expert relatively easily after the basic concepts [...] have been assimilated. This is a book that will be useful to many people and I can positively recommend it." (Brian L. Burrows, Mathematical Reviews 2002m)

Lectures on Nonextensive Statistical Mechanics
Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Statusp. 3
Introductionp. 3
Formalismp. 6
Theoretical Evidence and Connectionsp. 24
Experimental Evidence and Connectionsp. 38
Computational Evidence and Connectionsp. 55
Final Remarksp. 80
Quantum Density Matrix Description of Nonextensive Systemsp. 99
General Remarksp. 99
Theory of Entangled States and Its Implications: Jaynes-Cummings Modelp. 110
Variational Principlep. 124
Time-Dependence: Unitary Dynamicsp. 132
Time-Dependence: Nonunitary Dynamicsp. 147
Concluding Remarksp. 149
Referencesp. 154
Tsallis Theory, the Maximum Entropy Principle, and Evolution Equationsp. 157
Introductionp. 157
Jaynes Maximum Entropy Principlep. 159
General Thermostatistical Formalismsp. 161
Time Dependent MaxEntp. 168
Time-Dependent Tsallis MaxEnt Solutions of the Nonlinear Fokker-Planck Equationp. 170
Tsallis Nonextensive Thermostatistics and the Vlasov-Poisson Equationsp. 178
Conclusionsp. 188
Referencesp. 189
Computational Methods for the Simulation of Classical and Quantum Many Body Systems Sprung from Nonextensive Thermostatisticsp. 193
Background and Focusp. 193
Basic Properties of Tsallis Statisticsp. 195
General Properties of Mass Action and Kineticsp. 203
Tsallis Statistics and Simulated Annealingp. 209
Tsallis Statistics and Monte Carlo Methodsp. 214
Tsallis Statistics and Molecular Dynamicsp. 219
Optimizing the Monte Carlo or Molecular Dynamics Algorithm Using the Ergodic Measurep. 222
Tsallis Statistics and Feynman Path Integral Quantum Mechanicsp. 223
Simulated Annealing Using Cauchy-Lorentz ôDensity Packetö Dynamicsp. 228
Further Topics
Correlation Induced by Nonextensivity and the Zeroth Law of Thermodynamicsp. 237
Referencesp. 242
Dynamic and Thermodynamic Stability of Nonextensive Systemsp. 243
Introductionp. 243
Nonextensive Thermodynamicsp. 243
Nonlinear von Neumann Equationp. 244
Dynamic Stabilityp. 246
Thermodynamic Stabilityp. 247
Proof of Theorem 1p. 248
Minima of F(3)p. 249
Proof of Theorem 2p. 251
Conclusionsp. 251
Referencesp. 252
Generalized Simulated Annealing Algorithms Using Tsallis Statistics: Application to ±J Spin Glass Modelp. 253
Generalized Acceptance Probabilitiesp. 253
Model and Simulationsp. 254
Resultsp. 255
Summaryp. 257
Protein Folding Simulations by a Generalized-Ensemble Algorithm Based on Tsallis Statisticsp. 259
Introductionp. 259
Methodsp. 260
Resultsp. 263
Conclusionsp. 273
Referencesp. 273
Subject Indexp. 275
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540412083
ISBN-10: 3540412085
Series: Lecture Notes in Physics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 278
Published: January 2001
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.13 x 16.51  x 1.91
Weight (kg): 0.52

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