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This book presents the Proceedings of the 54th Winter School of Theoretical Physics on Simplicity of Complexity in Economic and Social Systems, held in Lądek Zdrój, Poland, from 18 to 24 February 2018. The purpose of the book is to introduce the new interdisciplinary research that links statistical physics, and particular attention is given to link physics of complex systems, with financial analysis and sociology. The main tools used in these areas are numerical simulation of agents behavior and the interpretation of results with the help of complexity methods, therefore a background in statistical physics and in physics of phase transition is necessary to take the first steps towards these research fields called econophysics and sociophysics. In this perspective, the book is intended to graduated students and young researchers who want to begin the study of this established new area, which connects physicists, economists, sociologists and IT professionals, tobetter understand complexity phenomena existing not only in physics but also in complex systems being seemingly far from traditional view at physics.

Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces.This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.

This NATO Advanced Study Institute centered on large-scale molecular systems: Quantum mechanics, although providing a general framework for the description of matter, is not easily applicable to many concrete systems of interest; classical statistical methods, on the other hand, allow only a partial picture of the behaviour of large systems. The aim of the ASI was to present both aspects of the subject matter and to foster interaction between the scientists working in these important areas of theoretical physics and theoretical chemistry. The quantum-mechanical part was mostly based on the operator-algebraic formulation of quantum mechanics and comprised quantum statistics of infinite systems with special em­ phasis on macroscopic observables, equilibrium conditions, irreversibility on the one hand, symmetry breaking for molecules in the radiation field and macroscopic quantum phenomena in the theory of superconductivity (BCS-theory) on the other hand. In addition, phase-space methods for many-body systems were also presented. Statistical physics was the main topic in the other lectures of the School; much emphasis was put on the statistical features of macros­ copic ('large') systems, the lectures dealt with mass and energy transport im polymers, in gels and in microemulsions, with aggregation and growth phenomena, with relaxation in complex, correlated systems, with conduction and optical properties of polymers, and with the means of describing disordered systems, above all fractals and related hierarchical models.

In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap­ proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

The surprising connections which have developed between physics and various fields as diverse as biology and economics now constitute the fascinating research area known as complex materials and systems. The study of complex materials and processes is rapidly expanding, and many important experimental and theoretical discoveries have been made in recent years. Statistical physics is key to exploring this new and expanding field, enabling an understanding of real-world phenomena compromised of complex materials or exhibiting complex processes. This book includes lectures presented at the CLXXVI International School of Physics “Enrico Fermi”, held in Varenna, Italy, in July 2010. The school focused on recent advances and developing perspectives in the study of complex materials and processes, as related to physics and biology. The book provides both an introduction and a complete presentation of recent theoretical and experimental developments for each topic. Topics addressed include: scaling and universality, supra-molecular systems and solutions, polymer systems, static and dynamics of liquid water, arrested dynamics and jamming, dynamics of out of equilibrium systems, physics of confined liquids, granular matter, physics of biological and medical systems, networks in physical and social sciences, turbulence in physics, biology and economics and finally, switching phenomena in biology and economics. The book provides reviews of these cutting edge topics by leading authorities and will be a reference work useful to both advanced research professionals and beginning graduate students.

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best'inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

The four-week period fran May 20 to June 16, 1984 was an intensive period of advanced study on the foundations and frontiers of nonequili­ brium statistical physics (NSP). During the first two weeks of this period, an advanced-study course on the'Foundations of NSP'was con­ ducted in Albuquerque under the sponsorship of the University of New Mexico Center for High-Technology Materials. This was followed by a two-week NATO Advanced Study Insti tute on the'Frontiers of NSP'in Santa Fe under the same directorship. Many Students attended both meetings. This book comprises proceedings based on those lectures and covering a broad spectrum of topics in NSP ranging fran basic problems in quantum measurement theory to analogies between lasers and Darwinian evolution. The various types of quantum distribution functions and their uses are treated by several authors. other tools of NSP, such as Langevin equations, Fokker-Planck equations, and master equations, are developed and applied to areas such as laser physics, plasma physics, Brownian motion, and hydrodynamic instabilities. The properties and experimental detection of squeezed states and antibunching are described, as well as experimental tests of the violation of Bell's inequality. Information theory, mean-field theory, reservoir theory, entropy maximization, and even a novel nonlinear generalization of quantum mechanics are used to discuss nonequilibrium phenanena and the approach toward thermodynamic equilibrium.

The primary goal of the book is to present the ideas and research findings of active researchers from various communities (physicists, economists, mathematicians, financial engineers) working in the field of'Econophysics', who have undertaken the task of modelling and analyzing order-driven markets. Of primary interest in these studies are the mechanisms leading to the statistical regularities ('stylized facts') of price statistics. Results pertaining to other important issues such as market impact, the profitability of trading strategies, or mathematical models for microstructure effects, are also presented. Several leading researchers in these fields report on their recent work and also review the contemporary literature. Some historical perspectives, comments and debates on recent issues in Econophysics research are also included.

The Conference on Statistical Physics, High Energy, Condensed Matter and Mathematical Physics was held in honor of Professor Chen-Ning Yang's 85th birthday in Singapore in Oct-Nov 2007. The conference paid tribute to the breadth and depth of Professor Yang's achievements in physics and science education since he received his Nobel Prize in Physics fifty years ago.This notable birthday volume is a collection of the presentations made at the conference by many eminent scientists who had worked closely with him or who have been influenced to some extent by his work.

Ludwig Eduard Boltzmann (1844–1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. To commemorate the 100th anniversary of his death in Duino, the International Symposium “Boltzmann's Legacy” was held at the Erwin Schrödinger International Institute for Mathematical Physics in June 2006. This text covers a wide spectrum of topics ranging from equilibrium statistical and nonequilibrium statistical physics, ergodic theory and chaos to basic questions of biology and historical accounts of Boltzmann's work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad overview of Boltzmann's legacy to the sciences from the standpoint of some of present day's leading scholars in the field. The book addresses students and researchers in mathematics, physics and the history of science.

Econophysicists have recently been quite successful in modelling and analysing various financial systems like trading, banking, stock and other markets. The statistical behaviour of the underlying networks in these systems have also been identified and characterised recently. This book reviews the current econophysics researches in the structure and functioning of these complex financial network systems. Leading researchers in the respective fields will report on their recent researches and review on the contemporary developments. The book will also include the comments and debates on the latest issues arising out of these

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.

Understanding the mechanism of a socio-economic system requires more than an understanding of the individuals that comprise the system. It also requires understanding how individuals interact with each other, and how the agg- gated outcome can be more than the sum of individual behaviors. This book contains the papers fostering the formation of an active multi-disciplinary community on socio-economic systems with the exciting new?elds of age- based modeling and econophysics. We especially intend to increase the awareness of researchers in many?elds with sharing the common view many economic and social activities as collectives of a large-scale heterogeneous and interacting agents. Economists seek to understand not only how individuals behave but also how the interaction of many individuals leads to complex outcomes. Age- based modeling is a method for studying socio-economic systems exhibiting the following two properties: (1) the system is composed of interacting agents, and (2) the system exhibits emergent properties, that is, properties arising from the interactions of the agents that cannot be deduced simply by agg- gating the properties of the system's components. When the interaction of the agents is contingent on past experience, and especially when the agents continually adapt to that experience, mathematical analysis is typically very limited in its ability to derive the outcome.

This book reviews the latest econophysics researches on the fluctuations in stock, forex and other markets. The statistical modeling of markets, using various agent-based game theoretical approaches, and their scaling analysis have been discussed. The leading researchers in these fields have reported on their recent work and also reviewed the contemporary literature. Some historical perspectives as well as some comments and debates on recent issues in econophysics research have also been included.

We all know the hard fact: neither wealth nor income is ever uniform for us all. Justified or not, they are unevenly distributed; few are rich and many are poor! Investigations for more than hundred years and the recent availability of the income distribution data in the internet (made available by the finance ministries of various countries; from the tax return data of the income tax departments) have revealed some remarkable features. Irrespective of many differences in culture, history, language and, to some extent, the economic policies followed in different countries, the income distribution is seen to fol­ low a particular universal pattern. So does the wealth distribution. Barring an initial rise in population with income (or wealth; for the destitutes), the population decreases either exponentially or in a log-normal way for the ma­ jority of'middle income'group, and it eventually decreases following a power law (Pareto law, following Vilfredo Pareto's observation in 1896) for the rich­ est 5-10% of the population! This seems to be an universal feature - valid for most of the countries and civilizations; may be in ancient Egypt as well! Econophysicists tried to view this as a natural law for a statistical ma- body-dynamical market system, analogous to gases, liquids or solids: classical or quantum.

Econophysics is a newborn field of science bridging economics and physics. A special feature of this new science is the data analysis of high-precision market data. In economics arbitrage opportunity is strictly denied; however, by observing high-precision data we can prove the existence of arbitrage opportunity. Also, financial technology neglects the possibility of market prediction; however, in this book you can find many examples of predicted events. There are other surprising findings. This volume is the proceedings of a workshop on'application of econophysics'at which leading international researchers discussed their most recent results.

Financial fluctuations were generally neglected in classical ecnomics and their basic statistical properties have only recently been elucidated in the emerging field of econophysics, a new science that analyzes data using methods developed by statistical physics, such as chaos, fractals, and phase transitions. This volume is the proceedings of a workshop at which leading international researchers in this discipline discussed their most recent results and examined the validity of the empirical laws of econophysics. Topics include stock market prices and foreign exchange rates, income distribution, market anomalies, and risk management. The papers herein relate econophysics to other models, present new models, and illustrate the mechanisms by which financial fluctuations occur using actual financial data. Containing the most recent econophysics results, this volume will serve as an indispensable reference for economic theorists and practitioners alike.

Investigation of the fractal and scaling properties of disordered systems has recently become a focus of great interest in research. Disordered or amorphous materials, like glasses, polymers, gels, colloids, ceramic superconductors and random alloys or magnets, do not have a homogeneous microscopic structure. The microscopic environment varies randomly from site to site in the system and this randomness adds to the complexity and the richness of the properties of these materials. A particularly challenging aspect of random systems is their dynamical behavior. Relaxation in disordered systems generally follows an unusual time-dependent trajectory. Applications of scaling and fractal concepts in disordered systems have become a broad area of interdisciplinary research, involving studies of the physics, chemistry, mathematics, biology and engineering aspects of random systems.This book is intended for specialists as well as graduate and postdoctoral students working in condensed-matter or statistical physics. It provides state-of-the-art information on the latest developments in this important and timely topic. The book is divided into three parts: Part I deals with critical phenomena, Part II is devoted to discussion of slow dynamics and Part III involves the application of scaling concepts to random systems. The effects of disorder at the mesoscopic scale as well as the latest results on the dynamical properties of disordered systems are presented. In particular, recent developments in static and dynamic scaling theories and applications of fractal concepts to disordered systems are discussed.

This volume contains research and review papers on different branches of mathematics and mathematical physics, written by the leading specialists. Among the contributed papers are articles on: (i) multiple basic hypergeometric functions with applications to the number theory, (ii) birational representations of affine Weyl groups with applications to discrete integrable systems, (iii) algebraic geometry and Painleve VI, and (iv) combinatorics of Kostka-Foulkes polynomials.

In these proceedings, it is shown that thermodynamical concepts are not ‘old fashioned'but still are most useful at the frontiers of modern science. Among the contributors are well-known experts such as Andresen (Copenhagen), Eu (Montreal), Groβmann (Marburg), Kawasaki (Fuhuoha), Maugin (Paris), Nicolis (Bruxelles) and Szépfalusy (Budapest). The subject covers a wide field including: recent developments in phenomenological thermodynamics, statistical foundation of thermodynamical concepts, thermodynamical concepts in nonlinear dynamics, applications to nonlinear (neural) networks, stochastic theory and transition processes.

The International Conference on the Progress in Statistical Physics was held in commemoration of Professor Choh, who is renowned for his seminal contribution to the kinetic theory of non-dilute fluids, well known as the Choh-Uhlenbeck equation. During the conference, some of the remarkable progress in the field of statistical physics were reviewed and future directions of statistical physics was discussed.

These proceedings comprise the invited lectures and an edited sampling of few other contributions to the 4th Teaching Modern Physics Conference held in Badajoz (Spain) on July 1992, devoted to THERMODYNAMICS AND STATISTICAL PHYSICS: CRITICAL PHENOMENA, PHASE TRANSITIONS, NONLINEAR EVOLUTION, FRACTALS, COMPLEXITY,… COMPUTER SIMULATIONS forms the core of the contents.

Statistical physics is one of the fundamental branches of modern science. It provides a useful tool constructing a bridge from the microscopic to the macroscopic world. In the last forty years, most of the extensive applications have been made successfully in a variety of fields, such as physics, chemistry, biology, materials science, and even astronomy, where many new concepts and methods have been developed.The purpose of this meeting is to provide an opportunity for young researchers in experimental, theoretical and computational fields to communicate with one another using the common language of statistical physics, and thus foster many-body interactions among themselves.

The 19th IUPAP International Conference on Statistical Physics is devoted to the general field of statistical physics, including traditional topics such as statistical methods concerning the static and dynamic properties of mesoscopic and macroscopic states of matter, as well as hot topics of current interest in applications of statistical physics. These include quantum chaos and turbulence, structures and patterns, fractals, neural networks, computer simulation and visualization in statistical physics, disordered systems and heterogeneous systems, simple and complex fluids.

This volume of proceedings of the XXII Winter Meeting on Statistical Physics provides an overview of the subjects of current interest in statistical physics. Topics discussed include analytical as well as computer studies of the equilibrium properties of fluids, electrolytes, dense polymer systems and colloidal mixtures, proton transfer dynamics, chaos in cellular automata, sandpile physics and avalanches, ballistic aggregation and the electric microfield in a plasma.