Introduction to nonextensive statistical mechanics: approaching a complex world
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 382 Seiten Illustrationen, Diagramme |
| ISBN: | 9781441927484 |
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MARC
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| 245 | 1 | 0 | |a Introduction to nonextensive statistical mechanics |b approaching a complex world |c Constantino Tsallis |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XVIII, 382 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Statistical mechanics | |
| 650 | 0 | 7 | |a Statistische Physik |0 (DE-588)4057000-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804138562284683264 |
|---|---|
| adam_text | Contents
Part I Basics or How the Theory Works
1
Historical Background and Physical Motivations
................... 3
1.1
Introduction
................................................ 3
1.2
Background and Indications in the Literature
.................... 6
1.3
Symmetry, Energy, and Entropy
............................... 12
1.4
A Few Words on the Foundations of Statistical Mechanics
......... 13
Learning with Boltzmann-Gibbs Statistical Mechanics
.............. 19
2.1
Boltzmann-Gibbs Entropy
................................... 19
2.1.1 Entropie
Forms
..................................... 19
2.1.2
Properties
.......................................... 21
2.2
Kullback-Leibler Relative Entropy
............................ 28
2.3
Constraints and Entropy Optimization
.......................... 30
2.3.1
Imposing the Mean Value of the Variable
................ 30
2.3.2
Imposing the Mean Value of the Squared Variable
........ 31
2.3.3
Imposing the Mean Values of both the Variable
and Its Square
...................................... 32
2.3.4
Others
............................................. 33
2.4
Boltzmann-Gibbs Statistical Mechanics and Thermodynamics
..... 33
2.4.
і
Isolated System
-
Microcanonical Ensemble
............. 35
2.4.2
In the Presence of a Thermostat
-
Canonical Ensemble
.... 35
2.4.3
Others
............................................. 36
Generalizing What We Learnt:
Nonextensive
Statistical Mechanics
... 37
3.1
Playing with Differential Equations
-
A Metaphor
............... 37
3.2 Nonadditive
Entropy
St¡
...................................... 41
3.2.1
Definition
.......................................... 41
3.2.2
Properties
.......................................... 43
xvi Contents
3.3
Correlations, Occupancy of Phase-Space, and Extensivity of Sc/
.... 54
3.3.1
A Remark on the Thermodynamical Limit
............... 54
3.3.2
The (/-Product
...................................... 61
3.3.3
The q-Sum
......................................... 64
3.3.4
Extensivity of Sq
-
Effective Number of States
........... 66
3.3.5
Extensivity of Sq
-
Binary Systems
..................... 69
3.3.6
Extensivity of S4
-
Physical Realizations
................ 77
3.4
q
-Generalization of the Kullback-Leibler Relative Entropy
........ 84
3.5
Constraints and Entropy Optimization
.......................... 88
3.5.1
Imposing the Mean Value of the Variable
................ 88
3.5.2
Imposing the Mean Value of the Squared Variable
........ 89
3.5.3
Others
............................................. 90
3.6 Nonextensive
Statistical Mechanics and Thermodynamics
......... 90
3.7
About the Escort Distribution and the
g
-Expectation Values
....... 98
3.8
About Universal Constants in Physics
..........................102
3.9
Various Other
Entropie
Forms
................................105
Part II Foundations or Why the Theory Works
4
Stochastic Dynamical Foundations of
Nonextensive
Statistical
Mechanics
.....................................................109
4.1
Introduction
................................................109
4.2
Normal Diffusion
...........................................110
4.3
Levy Anomalous Diffusion
...................................
Ill
4.4
Correlated Anomalous Diffusion
..............................
Ill
4.4.1
Further Generalizing the Fokker-Planck Equation
........117
4.5
Stable Solutions of Fokker-Planck-Like Equations
...............117
4.6
Probabilistic Models with Correlations
-
Numerical
and Analytical Approaches
.................................. 119
4.6.1
The MTG Model and Its Numerical Approach
...........120
4.6.2
The TMNT Model and Its Numerical Approach
..........125
4.6.3
Analytical Approach of the MTG and TMNT Models
.....129
4.6.4
The RST1 Model and Its Analytical Approach
...........132
4.6.5
The RST2 Model and Its Numerical Approach
...........
1
33
4.7
Central Limit Theorems
......................................135
4.8
Generalizing the
Langevin
Equation
...........................144
4.9
Time-Dependent Ginzburg-Landau ¿/-Dimensional O(n)
Ferromagnet with
n
=
d
.................................... 149
5
Deterministic Dynamical Foundations of
Nonextensive
Statistical
Mechanics
.....................................................151
5.1
Low-Dimensional Dissipative Maps
...........................151
5.1.1
One-Dimensional Dissipative Maps
....................151
5.1.2
Two-Dimensional Dissipative Maps
....................164
Contents
5.2
Low-Dimensional Conservative Maps
..........................165
5.2.1
Strongly Chaotic Two-Dimensional Conservative Maps.
... 166
5.2.2
Strongly Chaotic Four-Dimensional Conservative
Maps
............................................. 172
5.2.3
Weakly Chaotic Two-Dimensional Conservative Maps
....173
5.3
High-Dimensional Conservative Maps
.........................179
5.4
Many-Body Long-Range-Interacting Hamiltonian Systems
........182
5.4.1
Metastability, Nonergodicity, and Distribution
of Velocities
....................................... 186
5.4.2
Lyapunov Spectrum
.................................186
5.4.3
Aging and Anomalous Diffusion
.......................188
5.4.4
Connection with Glassy Systems
.......................190
5.5
The
</
-Triplet
...............................................191
5.6
Connection with Critical Phenomena
...........................195
5.7
A Conjecture on the Time and Size Dependences of Entropy
.......196
Generalizing
Nonextensive
Statistical Mechanics
...................209
6.1
Crossover Statistics
.........................................209
6.2
Further Generalizing
........................................211
6.2.1
Spectral Statistics
...................................212
6.2.2
Beck-Cohen Superstatistics
...........................216
Part III Applications or What for the Theory Works
7
Thermodynamical and Nonthermodynamical Applications
..........221
7.1
Physics
....................................................222
Cold Atoms in Optical Lattices
........................222
High-Energy Physics
................................223
Turbulence
.........................................227
Fingering
..........................................233
Granular Matter
.....................................233
Condensed Matter Physics
............................235
Plasma
............................................237
Astrophysics
.......................................241
Geophysics
.........................................244
Quantum Chaos
.....................................254
Quantum Entanglement
..............................255
7.1.12
Random Matrices
...................................255
7.2
Chemistry
.................................................258
7.2.1
Generalized Arrhenius Law and Anomalous Diffusion
.....258
7.2.2
Lattice
Lotka-
Volterra Model for Chemical Reactions
and Growth
........................................ 259
7.2.3
Re-Association in Folded Proteins
.....................263
7.
.1
7.
.2
7.1.3
7.
.4
7.
.5
7.
.6
7.
.7
7.
.8
7.
.9
7.
.10
7.
.11
і
Contents
7.2.4
Ground State Energy of the Chemical Elements
(Mendeleev s Table) and of Doped
Fullerenes
........... 265
7.3
Economics
.................................................266
7.4
Computer Sciences
..........................................269
7.4.1
Optimization Algorithms
.............................269
7.4.2
Analysis of Time Series and Signals
....................275
7.4.3
Analysis of Images
..................................279
7.4.4
PING Internet Experiment
............................280
7.5
Biosciences
................................................281
7.6
Cellular Automata
..........................................282
7.7
Self-Organized Criticality
....................................283
7.8
Scale-Free Networks
........................................283
7.8.1
The Natal Model
....................................290
7.8.2
Albert-Barabasi Model
...............................291
7.8.3
Non-Growing Model
.................................294
7.8.4
Lennard-Jones Cluster
...............................295
7.9
Linguistics
.................................................295
7.10
Other Sciences
.............................................295
Part IV Last (But Not Least)
8
Final Comments and Perspectives
.................................305
8.1
Falsifiable Predictions and Conjectures, and Their Verifications
.... 305
8.2
Frequently Asked Questions
..................................308
8.3
Open Questions
............................................326
Appendix A Useful Mathematical Formulae
.........................329
Appendix
В
Escort Distributions and ^-Expectation Values
............335
B.I First Example
..............................................335
B.2 Second Example
............................................339
B.3 Remarks
..................................................339
Bibliography
.......................................................343
Index
.............................................................381
|
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| id | DE-604.BV035273660 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:10Z |
| institution | BVB |
| isbn | 9781441927484 |
| language | English |
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| physical | XVIII, 382 Seiten Illustrationen, Diagramme |
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| spelling | Tsallis, Constantino Verfasser (DE-588)138087962 aut Introduction to nonextensive statistical mechanics approaching a complex world Constantino Tsallis New York, NY Springer 2009 XVIII, 382 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Statistical mechanics Statistische Physik (DE-588)4057000-9 gnd rswk-swf Statistische Physik (DE-588)4057000-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017078988&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tsallis, Constantino Introduction to nonextensive statistical mechanics approaching a complex world Statistical mechanics Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 |
| title | Introduction to nonextensive statistical mechanics approaching a complex world |
| title_auth | Introduction to nonextensive statistical mechanics approaching a complex world |
| title_exact_search | Introduction to nonextensive statistical mechanics approaching a complex world |
| title_full | Introduction to nonextensive statistical mechanics approaching a complex world Constantino Tsallis |
| title_fullStr | Introduction to nonextensive statistical mechanics approaching a complex world Constantino Tsallis |
| title_full_unstemmed | Introduction to nonextensive statistical mechanics approaching a complex world Constantino Tsallis |
| title_short | Introduction to nonextensive statistical mechanics |
| title_sort | introduction to nonextensive statistical mechanics approaching a complex world |
| title_sub | approaching a complex world |
| topic | Statistical mechanics Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistical mechanics Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017078988&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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