Auger / Klir Dynamics and Thermodynamics in Hierarchically Organized Systems

Applications in Physics, Biology and Economics
1. Auflage 2013
ISBN: 978-1-4832-8727-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 223 Seiten, Web PDF

One of the most fundamental and efficient ways of conceptualizing complex systems is to organize them hierarchically. A hierarchically organized system is represented by a network of interconnected subsystems, each of which has its own network of subsystems, and so on, until some elementary subsystems are reached that are not further decomposed. This original and important book proposes a general mathematical theory of a hierarchical system and shows how it can be applied to very different topics such as physics (Hamiltonian systems), biology (coupling the molecular and the cellular levels), ecology (coupling the individual, population and ecosystem), and economics (coupling the sectoral, regional and national levels). The first attempt to develop mathematical frameworks for conceptualizing such systems only appeared in the early 1970s, and it took another decade before these mathematical frameworks were applied to various specific contexts of the sciences of the natural. Much of this work has been pioneered by the author, and he presents a more thorough work which will have a major impact on shifting current thinking in the sciences of the natural to a more holistic basis in which several levels of hierarchically organized systems are viewed in an integrated fashion.

Autoren/Hrsg.

Auger, P.

Klir, George J.

Inhaltsverzeichnis

1;Front Cover;1
2;Dynamics and Thermodynamics in Hierarchically Organized Systems: Applications in Physics, Biology and Economics;4
3;Copyright Page;5
4;Table of Contents;10
5;Dedication;8
6;Foreword;6
7;Introduction;14
8;CHAPTER 1. HIERARCHICALLY ORGANIZED HAMILTONIAN SYSTEMS;20
8.1;1. KINETIC ENERGY;20
8.2;2. POTENTIAL ENERGY;23
8.3;3. HAMILTONIAN;27
8.4;4. EQUATIONS FOR GROUP MOTION AND FOR INTERNAL MOTION;28
8.5;5. FAST VARYING GROUP VARIABLES, SLOW VARYING INTERNAL VARIABLES;32
8.6;6. COUPLINGS BETWEEN GROUP MOTION AND INTERNAL MOTION;33
8.7;7. FREE ENERGY AND ENTROPY OF A HIERARCHICAL SYSTEM;37
8.8;8. THREE LEVEL SYSTEM;40
9;CHAPTER 2. POPULATION DYNAMICS IN A HIERARCHICALLY ORGANIZED SYSTEM;42
9.1;1. EMERGENCE OF THE HIERARCHICAL LEVELS;42
9.2;2. TWO LEVEL SYSTEM;53
9.3;3. THREE LEVEL SYSTEM;76
10;CHAPTER 3. COUPLINGS BETWEEN THE BIOCHEMICAL
AND THE CELLULAR LEVELS;86
10.1;l.COUPLED CHEMICAL AND CELLULAR KINETICS;87
10.2;2. RELATIONS BETWEEN CELLULAR AGING RATES AND CHEMICAL RATES;93
10.3;3. MULTI-CELLULAR SYSTEM;109
11;CHAPTER 4. HIERARCHICALLY ORGANIZED POPULATION OF NEURONS;118
11.1;1. THE HOPFIELD MODEL;118
11.2;2. HIERARCHICALLY ORGANIZED POPULATION OF NEURONS;121
12;CHAPTER 5. HIERARCHICALLY ORGANIZED ECOSYSTEM;130
12.1;1. COUPLED INDIVIDUAL AND POPULATION KINETICS;130
12.2;2. COUPLED POPULATION AND ECOSYSTEM KINETICS;138
12.3;3. MICROEVOLUTION, MACROEVOLUTION;147
13;CHAPTER 6. HIERARCHICALLY ORGANIZED ECONOMICS;156
13.1;1. INPUT-OUTPUT ANALYSIS IN HIERARCHICALLY ORGANIZED ECONOMICS;156
13.2;2. COUPLED SECTORAL AND REGIONAL LEVELS;161
13.3;3. COUPLED SECTORAL, REGIONAL AND NATIONAL LEVELS;168
14;CHAPTER 7. Thermodynamics in a Hierarchically Organized System;174
14.1;1. MICROCANONICAL ENSEMBLE WITH EQUIPROBABLE STATES;175
14.2;2. MICROCANONICAL ENSEMBLE WITH NON-EQUIPROBABLE STATES;186
14.3;3. AN ECOLOGICAL EXAMPLE : COUPLED INDIVIDUAL AND POPULATION LEVELS;195
14.4;Conclusion;202
15;APPENDIX: MICROCANONICAL ENSEMBLES WITH
NON-EQUIPROBABLE STATES;206
15.1;MICROCANONICAL ENSEMBLE;206
15.2;ENSEMBLES WITH NON-EQUIPROBABLE STATES : AN ECOLOGICAL EXAMPLE;212
16;REFERENCES;216