This textbook provides a comprehensive, yet accessible, introduction to statistical mechanics. Crafted and class-tested over many years of teaching, it carefully guides advanced undergraduate and graduate students who are encountering statistical mechanics for the first time through this - sometimes - intimidating subject. The book provides a strong foundation in thermodynamics and the ensemble formalism of statistical mechanics. An introductory chapter on probability theory is included. Applications include degenerate Fermi systems, Bose-Einstein condensation, cavity radiation, phase transitions, and critical phenomena. The book concludes with a treatment of scaling theories and the renormalization group. In addition, it provides clear descriptions of how to understand the foundational mathematics and physics involved and includes exciting case studies of modern applications of the subject in physics and wider interdisciplinary areas. Key Features: Presents the subject in a clear and entertaining style which enables the author to take a sophisticated approach whilst remaining accessible Contains contents that have been carefully reviewed with a substantial panel to ensure that coverage is appropriate for a wide range of courses, worldwide Accompanied by volumes on thermodynamics and non-equilibrium statistical mechanics, which can be used in conjunction with this book, on courses which cover both thermodynamics and statistical mechanics

This book gathers together much of the author's work - both old and new - to explore a number of the key increases in complexity seen in the natural world, seeking to explain each of them purely in terms of the features of fitness landscapes. In a very straightforward manner, the book introduces basic concepts to help readers follow the main ideas. By using variations of the NK model and including the concept of the Baldwin effect, the author presents new abstract models that are able to explain why sources of evolutionary innovation (genomes, symbiosis, sex, chromosomes, multicellularity) have been selected for and hence how complexity has increased over time in some lineages.

The combined efforts of the Physicists and the Economists in recent years in a- lyzing and modeling various dynamic phenomena in monetary and social systems have led to encouragingdevelopments,generally classi?ed under the title of Eco- physics. These developmentsshare a commonambitionwith the alreadyestablished ?eld of Quantitative Economics. This volume intends to offer the reader a glimpse of these two parallel initiatives by collecting review papers written by well-known experts in the respective research frontiers in one cover. This massive book presents a unique combination of research papers contributed almost equally by Physicists and Economists. Additional contributions from C- puter Scientists and Mathematicians are also included in this volume. It consists of two parts: The ?rst part concentrates on econophysics of games and social choices and is the proceedings of the Econophys-Kolkata IV workshop held at the Indian Statistical Institute and the Saha Institute of Nuclear Physics, both in Kolkata, d- ing March 9-13, 2009. The second part consists of contributionsto quantitative e- nomics by experts in connection with the Platinum Jubilee celebration of the Indian Statistical Institute. In this connectiona Forewordfor the volume, written by Sankar K. Pal, Director of the Indian Statistical Institute, is put forth. Both parts specialize mostly on frontier problems in games and social choices. The?rst partofthebookdealswith severalrecentdevelopmentsineconophysics. Game theory is integral to the formulation of modern economic analysis. Often games display a situation where the social optimal could not be reached as a - sult of non co-operation between different agents.

The complete work consists of a two-volume set, describing two main classes of non-equilibrium phase-transitions, and surveys two main aspects of non-equilibrium phase-transitions: (a) transitions in the steady-state and (b) transitions in the relaxation behavior.Volume 1, Absorbing Phase Transitions, published in 2008, covered the statics and dynamics of transitions into an absorbing state. This volume 2 covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points. Aimed at researchers and graduate students in physics, the book is also suitable supplementary reading for advanced undergraduate students.

This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. It offers a critical overview of the research in this area and unifies the existing literature, employing a consistent notation. Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST quantization for constrained physical systems and its corresponding de Rham cohomology group structure. These were studied by theoretical physicists from the early 1960s and appeared in attempts to quantize rigorously some physical theories such as solitons and other models subject to geometrical constraints. In particular, phenomenological soliton theories such as Skyrmion and chiral bag models have seen a revival following experimental data from the SAMPLE and HAPPEX Collaborations and these are discussed. The book describes how these model predictions were shown to include rigorous treatments of geometrical constraints because these constraints affect the predictions themselves. The application of the BRST symmetry to the de Rham cohomology contributes to a deep understanding of Hilbert space of constrained physical theories. Aimed at graduate-level students in quantum field theory, the book will also serve as a useful reference for those working in the field. An extensive bibliography guides the reader towards the source literature on particular topics.

Robot and Multibody Dynamics: Analysis and Algorithms provides a comprehensive and detailed exposition of a new mathematical approach, referred to as the Spatial Operator Algebra (SOA), for studying the dynamics of articulated multibody systems. The approach is useful in a wide range of applications including robotics, aerospace systems, articulated mechanisms, bio-mechanics and molecular dynamics simulation. The book also: treats algorithms for simulation, including an analysis of complexity of the algorithms, describes one universal, robust, and analytically sound approach to formulating the equations that govern the motion of complex multi-body systems, covers a range of more advanced topics including under-actuated systems, flexible systems, linearization, diagonalized dynamics and space manipulators. Robot and Multibody Dynamics: Analysis and Algorithms will be a valuable resource for researchers and engineers looking for new mathematical approaches to finding engineering solutions in robotics and dynamics.

Providing a systematic introduction to the techniques which are fundamental to quantum field theory, this book pays special attention to the use of these techniques in a wide variety of areas, including ordinary quantum mechanics, quantum mechanics in the second-quantized formulation, relativistic quantum field theory, Euclidean field theory, quantum statistics at finite temperature, and the classical statistics of nonideal gas and spin systems. The extended chapter on variational methods and functional Legendre transformations contains completely original material.

Small systems are a very active area of research and development due to improved instrumentation that allows for spatial resolution in the range of sizes from one to 100 nm. In this size range, many physical and chemical properties change, which opens up new approaches to the study of substances and their practical application. This affects both traditional fields of knowledge and many other new fields including physics, chemistry, biology, etc. This book highlights new developments in statistical thermodynamics that answer the most important questions about the specifics of small systems - when one cannot apply equations or traditional thermodynamic models.

This book is the sixth volume of reviews on advanced problems of phase transitions and critical phenomena, with the first five volumes appearing in 2004, 2007, 2012, 2015, and 2018. It aims to provide an overview of those aspects of criticality and related topics that have attracted much attention due to the recent contributions. The six chapters discuss criticality of complex systems, where the new, emergent properties appear via collective behaviour of simple elements. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena provides a very natural conceptual and methodological framework for their study.As for the previous volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the 'Ising lectures' - a traditional annual workshop on phase transitions and critical phenomena which aims to bring together scientists working in the field of phase transitions with university students and those who are interested in the topic.The level of presentation makes the book readable both for professionals and the students in the field. On a larger scale, the book may contribute to promoting and deepening studies of phase transitions and critical phenomena.

These lecture notes cover Statistical Mechanics at the level of advanced undergraduates or postgraduates. After a review of thermodynamics, statistical ensembles are introduced, then applied to ideal gases, including degenerate gases of bosons and fermions, followed by a treatment of systems with interaction, of real gases, and of stochastic processes.The book offers a comprehensive and detailed, as well as self-contained, account of material that can and has been covered in a one-semester course for students with a basic understanding of thermodynamics and a solid background in classical mechanics.

These lecture notes cover Statistical Mechanics at the level of advanced undergraduates or postgraduates. After a review of thermodynamics, statistical ensembles are introduced, then applied to ideal gases, including degenerate gases of bosons and fermions, followed by a treatment of systems with interaction, of real gases, and of stochastic processes.The book offers a comprehensive and detailed, as well as self-contained, account of material that can and has been covered in a one-semester course for students with a basic understanding of thermodynamics and a solid background in classical mechanics.

The FIRST MEXICAN MEETING ON MATHEMATICAL AND EXPERI MENTAL PHYSICS was held at EL COLEGIO N ACIONAL in Mexico Cit y, Mexico, from September 10 to 14, 2001. This event consisted of the LEOPOLDO GARciA-COLiN SCHERER Medal Lecture, delivered by Prof. Nicholas G. van Kampen, a series of plenary talks by Leopoldo Garcia-Colin, Giinter Nimtz, Luis F. Rodriguez, Ruoon Barrera, and Donald Saari, and of three parallel symposia, namely, Cosmology and Gravitation, Statistical Physics and Beyond, and Hydrodynamics and Dynamical Systems. The response from the Physics community was enthusiastic, with over 200 participants and around 80 speakers, from allover the world: USA, Canada, Mexico, Germany, France, Holland, United Kingdom, Switzerland, Spain, and Hungary. The main aim of the conference is to provide a scenario to Mexican researchers on the topics of Mathematical and Experimental Physics in order to keep them in contact with work going on in other parts of the world and at the same time to motivate and support the young and mid career researchers from our country. To achieve this goal, we decided to the most distinguished experts in the subjects of the invite as lecturers conference and to give the opportunity to young scientist to communi cate the results of their work. The plan is to celebrate this international endeavor every three years."

This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications - Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a new approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharanov-Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.

This book discusses basic topics in the spectral theory of dynamical systems. It also includes two advanced theorems, one by H. Helson and W. Parry, and another by B. Host. Moreover, Ornstein's family of mixing rank-one automorphisms is given with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are also examined. Baire category theorems of ergodic theory, scattered in literature, are discussed in a unified way in the book. Riesz products are introduced and applied to describe the spectral types and eigenvalues of rank-one automorphisms. Lastly, the second edition includes a new chapter "Calculus of Generalized Riesz Products", which discusses the recent work connecting generalized Riesz products, Hardy classes, Banach's problem of simple Lebesgue spectrum in ergodic theory and flat polynomials.

The book covers all aspects from the expansion of the Boltzmann transport equation with harmonic functions to application to devices, where transport in the bulk and in inversion layers is considered. The important aspects of stabilization and band structure mapping are discussed in detail. This is done not only for the full band structure of the 3D k-space, but also for the warped band structure of the quasi 2D hole gas. Efficient methods for building the Schrodinger equation for arbitrary surface or strain directions, gridding of the 2D k-space and solving it together with the other two equations are presented."

social network analysis has been an established eld since the 1950s; in computer and information sciences, in biology, and of course in mathematics (graph theory) networks are central representations of objects and methods (De Nooy, forthc- ing). More detailed bibliometric studies have examined the individual, cognitive, and institutional composition of complex network theory (Morris and Yen 2004), and social network theory (Otte and Rousseau 2002). Among the more impor- .. tant pieces of literature are Borner et al. (2007), Bornholdt and Schuster (2003), Buchanan (2002), Dorogovtsev and Mendes (2003), Otte and Rousseau (2002), Newman (2003), and Watts (1999, 2004). Of these, Borner .. et al. (2007) stand out because they have most recently re-examined network science, considering it as a possible innovation in information science. All the reviews mentioned include efforts to build bridges between different scienti c disciplines and specialties. In this book we draw particular attention to the link between evolutionary economics and statistical physics. Despite this impressive development, claims that an entirely new science has been created (Barabasi ' 2002) have nevertheless been the subject of criticism. - depth analyses of a subset of "complex networks" contributions (1991-2003) have shown that the notion of "complex networks" was already prevalent in a number of different elds before it became practically a "brand name" or the popular label for a new specialty area in physics, or a new cross-disciplinary paradigm.

This book presents scientific metrics and its applications for approaching scientific findings in the field of Physics, Economics and Scientometrics. Based on a collection of the author's publications in these fields, the book reveals the profound links between the measures and the findings in the natural laws, from micro-particles to macro-cosmos, in the economic rules of human society, and in the core knowledge among mass information. With this book the readers can gain insights or ideas on addressing the questions of how to measure the physical world, economics process and human knowledge, from the perspective of scientific metrics. The book is also useful to scientists, particularly to specialists in physics, economics and scientometrics, for promoting and stimulating their creative ideas based on scientific metrics.

Starting from basic principles, the book covers a wide variety of topics, ranging from Heisenberg, Schroedinger, second quantization, density matrix and path integral formulations of quantum mechanics, to applications that are (or will be) corner stones of present and future technologies. The emphasis is on spin waves, quantum information, recent tests of quantum physics and decoherence. The book provides a large amount of information without unbalancing the flow of the main ideas by laborious detail.

This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.

Models for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that, in some cases, they may violate the laws of thermodynamics. In The Thermophysics of Porous Media, the author shows that physical consistency requires a unique description of dynamic processes that involve porous media, and that new dynamic variables-porosity, saturation, and megascale concentration-naturally enter into the large-scale description of porous media. The new degrees of freedom revealed in this study predict new dynamic processes that are not associated with compressional motions. The book details the construction of a Lorentz invariant thermodynamic lattice gas model and shows how the associated nonrelativistic, Galilean invariant model can be used to describe flow in porous media. The author develops the equations of seismic wave propagation in porous media, the associated boundary conditions, and surface waves. He also constructs the equations for both immiscible and miscible flows in porous media and their related instability problems. The implications of the physical theory presented in this book are significant, particularly in applications in geophysics and the petroleum industry. The Thermophysics of Porous Media offers a unique opportunity to examine the dynamic role that porosity plays in porous materials.

STATISTICAL PHYSICS AND ECONOMICS covers systematically and in simple language the physical foundations of evolution equations, stochastic processes, and generalized Master equations applied to complex economic systems. Strong emphasis is placed on concepts, methods, and techniques for modeling, assessment, and solving or estimation of economic problems in an attempt to understand the large variability of financial markets, trading and communication networks, barriers and acceleration of the economic growth as well as the kinetics of product and money flows. The main focus of the book is a clear physical understanding of the self-organizing principles in social and economic systems. This modern introduction will be a useful tool for researchers, engineers, as well as graduate and post-graduate students in econophysics and related topics.