A Concise Introduction to the Statistical Physics of Complex Systems (SpringerBriefs in Complexity)

This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. Â Indeed, in recent years, statistical physics has begun to attract the interest of a broad community of researchers in the field of complex system sciences, ranging from biology to the social sciences, economics and computer science. More generally, a growing number of graduate students and researchers feel the need to learn some basic concepts and questions originating in other disciplines without necessarily having to master all of the corresponding technicalities and jargon. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting âentitiesâ, and on the other to predict the macroscopic (or collective) behavior of the system considered from the microscopic laws ruling the dynamics of the individual âentitiesâ. These two goals are, to some extent, also shared by what is nowadays called âcomplex systems scienceâ and for these reasons, systems studied in the framework of statistical physics may be considered as among the simplest examples of complex systemsâ"allowing in addition a rather well developed mathematical treatment Cover page......Page 1 A Concise Introduction to the Statistical Physics of Complex Systems......Page 4 Preface......Page 6 Contents......Page 7 Introduction......Page 9 1.1.1 A Particle Attached to a Spring......Page 11 1.1.3 Case of Discrete Variables: Spin Models......Page 15 1.2.1 Notion of Statistical Description: A Toy Model......Page 16 1.2.2 Fundamental Postulate of Equilibrium Statistical Physics......Page 17 1.2.3 Computation of (E) and S(E): Some Simple Examples......Page 18 1.2.4 Distribution of Energy Over Subsystems and Statistical Temperature......Page 20 1.3.1 Exchanges of Energy......Page 22 1.3.2 Canonical Entropy......Page 25 1.3.3 Exchanges of Particles with a Reservoir: The Grand-Canonical Ensemble......Page 27 1.4.2 Ising Model in Fully Connected Geometry......Page 28 1.4.3 Ising Model with Finite Connectivity......Page 31 1.4.4 Renormalization Group Approach: A Brief Introduction......Page 32 1.5.1 Disorder in Complex Systems: From Social Sciences to Spin-Glasses......Page 37 1.5.3 The Simplest Disordered System: The Random Energy Model......Page 38 References......Page 41 2.1.1 Definition of Markovian Stochastic Processes......Page 42 2.1.2 Master Equation and Detailed Balance......Page 44 2.1.3 Dynamical Increase of the Entropy......Page 46 2.1.4 A Simple Example: The One-Dimensional Random Walk......Page 47 2.2.1 Phenomenological Approach to the Langevin Equation......Page 50 2.2.2 Relation to Random Walks......Page 54 2.2.3 Fokker--Planck Equation......Page 56 2.3.1 Generalized Central Limit Theorem......Page 58 2.3.2 Anomalous Diffusion......Page 61 2.3.3 Aging Dynamics and Trap Models......Page 63 References......Page 66 3 Statistical Physics of Interacting Macroscopic ``Entities''......Page 67 3.1 Dynamics of Residential Moves......Page 68 3.1.2 Equilibrium Configurations of the Model......Page 69 3.1.3 Condition for Phase Separation......Page 71 3.2 Condensation Transition......Page 73 3.2.2 Maximal Density and Condensation Phenomenon......Page 74 3.3 Synchronization Transition......Page 75 3.3.1 The Kuramoto Model of Coupled Oscillators......Page 76 3.3.2 Synchronized Steady State......Page 78 3.4 Collective Motion of Active Particles......Page 80 3.4.2 Description Through a Boltzmann Equation......Page 81 3.4.3 Hydrodynamic Equations and Phase Diagram......Page 82 References......Page 85 This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. Â Indeed, in recent years, statistical physics has begun to attract the interest of a broad community of researchers in the field of complex system sciences, ranging from biology to the social sciences, economics and computer science. More generally, a growing number of graduate students and researchers feel the need to learn some basic concepts and questions originating in other disciplines without necessarily having to master all of the corresponding technicalities and jargon. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting âentitiesâ, and on the other to predict the macroscopic (or collective) behavior of the system considered from the microscopic laws ruling the dynamics of the individual âentitiesâ. These two goals are, to some extent, also shared by what is nowadays called âcomplex systems scienceâ and for these reasons, systems studied in the framework of statistical physics may be considered as among the simplest examples of complex systemsâ"allowing in addition a rather well developed mathematical treatment Annotation This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. Indeed, in recent years, statistical physics has begun to attract the interest of a broad community of researchers in the field of complex system sciences, ranging from biology to the social sciences, economics and computer science. More generally, a growing number of graduate students and researchers feel the need to learn some basic concepts and questions originating in other disciplines without necessarily having to master all of the corresponding technicalities and jargon. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting entities, and on the other to predict the macroscopic (or collective) behavior of the system considered from the microscopic laws ruling the dynamics of the individual entities. These two goals are, to some extent, also shared by what is nowadays called complex systems science and for these reasons, systems studied in the framework of statistical physics may be considered as among the simplest examples of complex systemsallowing in addition a rather well developed mathematical treatment Provides graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. This book summarizes the goals of statistical physics.