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Nonextensive Statistical Mechanics and Its Applications


Author(s): Abe, Sumiyoshi; Okamoto, Yuko
ISBN10:  3540412085
ISBN13:  9783540412083
Format:  Hardcover
Pub. Date:  2/1/2001
Publisher(s): Springer Verlag

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SummaryTable of Contents
A generalization of the well-know Boltzman-Gibbs theory, featuring a set of self-contained lectures and additional contributions covering some of the latest developments in nonextensive statistical mechanics and its applications. Addresses graduate students, lecturers and researchers.
Part 1 Lectures on Nonextensive Statistical Mechanics
Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status
3(96)
C. Tsallis
Introduction
3(3)
Formalism
6(18)
Theoretical Evidence and Connections
24(14)
Experimental Evidence and Connections
38(17)
Computational Evidence and Connections
55(25)
Final Remarks
80(19)
Quantum Density Matrix Description of Nonextensive Systems
99(58)
A.K. Rajagopal
General Remarks
99(11)
Theory of Entangled States and Its Implications: Jaynes-Cummings Model
110(14)
Variational Principle
124(8)
Time-Dependence: Unitary Dynamics
132(15)
Time-Dependence: Nonunitary Dynamics
147(2)
Concluding Remarks
149(8)
References
154(3)
Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations
157(36)
A. R. Plastino
Introduction
157(2)
Jaynes Maximum Entropy Principle
159(2)
General Thermostatistical Formalisms
161(7)
Time Dependent MaxEnt
168(2)
Time-Dependent Tsallis MaxEnt Solutions of the Nonlinear Fokker-Planck Equation
170(8)
Tsallis Nonextensive Thermostatistics and the Vlasov-Poisson Equations
178(10)
Conclusions
188(5)
References
189(4)
Computational Methods for the Simulation of Classical and Quantum Many Body Systems Sprung from Nonextensive Thermostatistics
193(44)
I. Andricioaei
J.E. Straub
Background and Focus
193(2)
Basic Properties of Tsallis Statistics
195(8)
General Properties of Mass Action and Kinetics
203(6)
Tsallis Statistics and Simulated Annealing
209(5)
Tsallis Statistics and Monte Carlo Methods
214(5)
Tsallis Statistics and Molecular Dynamics
219(3)
Optimizing the Monte Carlo or Molecular Dynamics Algorithm Using the Ergodic Measure
222(1)
Tsallis Statistics and Feynman Path Integral Quantum Mechanics
223(5)
Simulated Annealing Using Cauchy-Lorentz ``Density Packet'' Dynamics
228(9)
Part 2 Further Topics
Correlation Induced by Nonextensivity and the Zeroth Law of Thermodynamics
237(6)
S. Abe
References
242(1)
Dynamic and Thermodynamic Stability of Nonextensive Systems
243(10)
J. Naudts
M. Czachor
Introduction
243(1)
Nonextensive Thermodynamics
243(1)
Nonlinear von Neumann Equation
244(2)
Dynamic Stability
246(1)
Thermodynamic Stability
247(1)
Proof of Theorem 1
248(1)
Minima of F(3)
249(2)
Proof of Theorem 2
251(1)
Conclusions
251(2)
References
252(1)
Generalized Simulated Annealing Algorithms Using Tsallis Statistics: Application to ±J Spin Glass Model
253(6)
J. Klos
S. Kobe
Generalized Acceptance Probabilities
253(1)
Model and Simulations
254(1)
Results
255(2)
Summary
257(2)
Protein Folding Simulations by a Generalized-Ensemble Algorithm Based on Tsallis Statistics
259(16)
Y. Okamoto
U.H.E. Hansmann
Introduction
259(1)
Methods
260(3)
Results
263(10)
Conclusions
273(2)
References
273(2)
Subject Index 275

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