Nonextensive Statistical Mechanics and Its Applications

by Abe, Sumiyoshi; Okamoto, Yuko

• ISBN13: 9783540412083
• ISBN10: 3540412085
• Format: Hardcover
• Copyright: 2001-02-01
• Publisher: Springer Verlag

Summary

Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the research of the foundations of statistical mechanics. This generalization of the well-known Boltzmann--Gibbs theory enables the study of systems with long-range interactions, long-term memories or multi-fractal structures. This book consists of a set of self-contained lectures and includes additional contributions where some of the latest developments -- ranging from astro- to biophysics -- are covered. Addressing primarily graduate students and lecturers, this book will also be a useful reference for all researchers working in the field.

Table of Contents

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