A Concise Introduction to the Statistical Physics of Complex Systems

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 systems—allowing in addition a rather well developed mathematical treatment.

• Complex systems modeling
• Interdisciplinary physics
• Schelling model
• Self-propelled particles
• Statistical physics primer
• Synchronization and Kuramoto model
• complexity
• systems biology

From the reviews:

“The well-written 77 pages long book is based on introductory lectures given by the author at summer schools on complex systems for participants of different branches with an interest in complex system modeling and on extended lectures given for master courses at universities. … The monograph is a good introduction to basic concepts of statistical physics and complex systems for students and researchers with an interest in complex systems in other fields … .” (Georg Hebermehl, Zentralblatt MATH, Vol. 1237, 2012)

“This short expository text intends to convey the basic ideas connecting statistical mechanics (microscopic level) with thermodynamics (macroscopic level). Its primary audience is composed of researchers coming from different origins and working in the area of complex systems. … Although there are more exhaustive and mathematically rigorous monographs treating various topics covered here (references are indicated below), this short text remains very refreshing for the mathematician.” (Dimitri Petritis, Mathematical Reviews, Issue 2012 k)

• Laboratoire de Physique, Ecole Normale Supérieure de Lyon, Lyon, France

  Eric Bertin

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