Statistical mechanics: the bane of many a physics student, and traditionally viewed as a long parade of ensembles, partition functions, and partial derivatives. But the subject needn't be arcane. When pared back to its underlying concepts and built from the ground up, statistical mechanics takes on a charm of its own, and sheds light on all manner of physical phenomena. This book presents a straightforward introduction to the key concepts in statistical mechanics, following the popular style of the author's highly successful textbook "Explorations in Mathematical Physics". Offering a clear, conceptual approach to the subject matter, the book presents a treatment that is mathematically complete, while remaining very accessible to undergraduates. It commences by asking: why does an ink drop spread out in a bathtub of water? This showcases the importance of counting configurations, which leads naturally to ideas of microstates, energy, entropy, thermodynamics, and physical chemistry. With this foundation, the Boltzmann distribution writes itself in its fullest form, and this opens the door to the Maxwell distribution and related areas of thermal conductivity and viscosity. Quantum ideas then appear: bosons via Einstein's and Debye's theories of heat capacity, and fermions via electrical conduction and low-temperature heat capacity of metals. The text ends with a detailed derivation of blackbody radiation, and uses this to discuss the greenhouse effect, lasers, and cosmology. Suitable for use with core undergraduate courses in statistical mechanics and thermodynamics, this book concentrates on using solid mathematics, while avoiding cumbersome notation. All the necessary mathematical steps are included in the body of the text and in the worked examples. Reviews of Explorations in Mathematical Physics by Don Koks, 2006 "With enjoyable and sometimes surprising excursions along the way, the journey provides a fresh look at many familiar topics, as it takes us from basic linear mathematics to general relativity... look forward to having your geometric intuition nourished and expanded by the author's intelligent commentaries." (Eugen Merzbacher, University of North Carolina) "... an interesting supplement to standard texts for teaching mathematical methods in physics, as it will add alternative views that could serve as additional material." (S. Marcelja, Australian Journal of Physics) "... a tour through the main ideas forming the language of modern mathematical physics ...it is a difficult task for the author to decide what is a good balance between the topics and their presentation, but in this case it has been achieved. ...for those physicists who would like to be exposed to clear motivation and careful explanation of the basics of the present-day apparatus of mathematical physics." (Ivailo Mladenov, Mathematical Reviews).

Statistical thermodynamics and the related domains of statistical physics and quantum mechanics are very important in many fields of research, including plasmas, rarefied gas dynamics, nuclear systems, lasers, semiconductors, superconductivity, ortho- and para-hydrogen, liquid helium, and so on. Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems provides a detailed overview of how to apply statistical principles to obtain the physical and thermodynamic properties of macroscopic systems. Intended for physics, chemistry, and other science students at the graduate level, the book starts with fundamental principles of statistical physics, before diving into thermodynamics. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and Lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The book concludes with an examination of statistical thermodynamics using functional integration and Feynman path integrals, and includes a wide range of problems with solutions that explain the theory.

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.

This volume explores the complex problems that arise in the modeling and simulation of crowd dynamics in order to present the state-of-the-art of this emerging field and contribute to future research activities. Experts in various areas apply their unique perspectives to specific aspects of crowd dynamics, covering the topic from multiple angles. These include a demonstration of how virtual reality may solve dilemmas in collecting empirical data; a detailed study on pedestrian movement in smoke-filled environments; a presentation of one-dimensional conservation laws with point constraints on the flux; a collection of new ideas on the modeling of crowd dynamics at the microscopic scale; and others. Applied mathematicians interested in crowd dynamics, pedestrian movement, traffic flow modeling, urban planning, and other topics will find this volume a valuable resource. Additionally, researchers in social psychology, architecture, and engineering may find this information relevant to their work.

This book introduces readers to essential tools for the measurement and analysis of information loss in signal processing systems. Employing a new information-theoretic systems theory, the book analyzes various systems in the signal processing engineer's toolbox: polynomials, quantizers, rectifiers, linear filters with and without quantization effects, principal components analysis, multirate systems, etc. The user benefit of signal processing is further highlighted with the concept of relevant information loss. Signal or data processing operates on the physical representation of information so that users can easily access and extract that information. However, a fundamental theorem in information theory-data processing inequality-states that deterministic processing always involves information loss. These measures form the basis of a new information-theoretic systems theory, which complements the currently prevailing approaches based on second-order statistics, such as the mean-squared error or error energy. This theory not only provides a deeper understanding but also extends the design space for the applied engineer with a wide range of methods rooted in information theory, adding to existing methods based on energy or quadratic representations.

This book presents recent results of basic research in the field of Raman scattering by optic and acoustic phonons in semiconductors, quantum wells and superlattices. It also describes various new applications for analytical materials research which have emerged alongside with scientific progress. Trends in Raman techniques and instrumentation and their implications for future developments are illustrated.

The first part is devoted to colloidal particles and stochastic dynamics, mainly concerned with recent authoritative results in the study of interactions between colloidal particles and transport properties in colloids and ferrocolloids. Recent advances in non-equilibrium statistical physics, such as stochastic resonance, Brownian motors, ratchets and noise-induced transport are also reported. The second part deals with biological systems and polymers. Here, standard simulation methodology to treat diffusional dynamics of multi-protein systems and proton transport in macromolecules is presented. Results of nervous system, spectroscopy of biological membrane models, and Monte Carlo simulations of polymers chains are also discussed. The third part is concerned with granular materials and quantum systems, in particular an effective-medium theory for a random system is reported. Additionally, a comprehensive treatment of spin and charge order in the vortex lattice of the cuprates, both theoretical and experimental, is included. Thermodynamics analogies between Bose-Einstein condensation and black-body radiation are also presented. The last part of the book contains recent developments of certain topics of liquid crystals and molecular fluids, including nonequilibrium thermal light scattering from nematic liquid crystals, relaxation in the kinetic Ising model on the periodic in homogeneous chain, models for thermotropic liquid-crystals, thermodynamic properties of fluids with discrete potentials as well as of fluids determined from the speed of sound effective potentials, and second viral coefficient for polar fluids.

In this book, the major ideas behind Organic Computing are delineated, together with a sparse sample of computational projects undertaken in this new field. Biological metaphors include evolution, neural networks, gene-regulatory networks, networks of brain modules, hormone system, insect swarms, and ant colonies. Applications are as diverse as system design, optimization, artificial growth, task allocation, clustering, routing, face recognition, and sign language understanding.

Random walks often provide the underlying mesoscopic mechanism for transport phenomena in physics, chemistry and biology. In particular, anomalous transport in branched structures has attracted considerable attention. Combs are simple caricatures of various types of natural branched structures that belong to the category of loopless graphs. The comb model was introduced to understand anomalous transport in percolation clusters. Comb-like models have been widely adopted to describe kinetic processes in various experimental applications in medical physics and biophysics, chemistry of polymers, semiconductors, and many other interdisciplinary applications.The authors present a random walk description of the transport in specific comb geometries, ranging from simple random walks on comb structures, which provide a geometrical explanation of anomalous diffusion, to more complex types of random walks, such as non-Markovian continuous-time random walks. The simplicity of comb models allows to perform a rigorous analysis and to obtain exact analytical results for various types of random walks and reaction-transport processes.

This authoritative text offers a complete overview on the statistical mechanics and electrodynamics of physical processes in dense plasma systems. The author emphasizes laboratory-based experiments and astrophysical observations of plasma phenomena, elucidated through the fundamentals. The coverage encompasses relevant condensed matter physics, atomic physics, nuclear physics, and astrophysics, including such key topics as phase transitions, transport, optical and nuclear processes. This essential resource also addresses exciting, cutting edge topics in the field, including metallic hydrogen, stellar and planetary magnetisms, pycnonuclear reactions, and gravitational waves. Scientists, researchers, and students in plasma physics, condensed matter physics, materials science, atomic physics, nuclear physics, and astrophysics will benefit from this work. Setsuo Ichimaru is a distinguished professor at the University of Tokyo, and has been a visiting member at The Institute for Advanced Study in Princeton, New Jersey, at the University of California, San Diego (UCSD), the Institute for Theoretical Physics at Johannes Kepler University, and the Max Planck Institute for Quantum Optics. He is a recipient of the Subramanyan Chandrasekhar Prize of Plasma Physics from the Association of Asia-Pacific Physical Societies and the Humboldt Research Award from the Alexander von Humboldt Foundation.

This authoritative text offers a complete overview on the statistical mechanics and electrodynamics of physical processes in dense plasma systems. The author emphasizes laboratory-based experiments and astrophysical observations of plasma phenomena, elucidated through the fundamentals. The coverage encompasses relevant condensed matter physics, atomic physics, nuclear physics, and astrophysics, including such key topics as phase transitions, transport, optical and nuclear processes. This essential resource also addresses exciting, cutting edge topics in the field, including metallic hydrogen, stellar and planetary magnetisms, pycnonuclear reactions, and gravitational waves. Scientists, researchers, and students in plasma physics, condensed matter physics, materials science, atomic physics, nuclear physics, and astrophysics will benefit from this work. Setsuo Ichimaru is a distinguished professor at the University of Tokyo, and has been a visiting member at The Institute for Advanced Study in Princeton, New Jersey, at the University of California, San Diego (UCSD), the Institute for Theoretical Physics at Johannes Kepler University, and the Max Planck Institute for Quantum Optics. He is a recipient of the Subramanyan Chandrasekhar Prize of Plasma Physics from the Association of Asia-Pacific Physical Societies and the Humboldt Research Award from the Alexander von Humboldt Foundation.

Communication-Protocol-Based Filtering and Control of Networked Systems is a self-contained treatment of the state of the art in communication-protocol-based filtering and control; recent advances in networked systems; and the potential for application in sensor networks. This book provides new concepts, new models and new methodologies with practical significance in control engineering and signal processing. The book first establishes signal-transmission models subject to different communication protocols and then develops new filter design techniques based on those models and preset requirements for filtering performance. The authors then extend this work to finite-horizon H-infinity control, ultimately bounded control and finite-horizon consensus control. The focus throughout is on three typical communications protocols: the round-robin, random-access and try-once-and-discard protocols, and the systems studied are drawn from a variety of classes, among them nonlinear systems, time-delayed and time-varying systems, multi-agent systems and complex networks. Readers are shown the latest techniques-recursive linear matrix inequalities, backward recursive difference equations, stochastic analysis and mapping methods. The unified framework for communication-protocol-based filtering and control for different networked systems established in the book will be of interest to academic researchers and practicing engineers working with communications and other signal-processing systems. Senior undergraduate and graduate students looking to increase their knowledge of current methods in control and signal processing of networked systems will also find this book valuable.

This book covers the broad subject of equilibrium statistical mechanics along with many advanced and modern topics such as nucleation, spinodal decomposition, inherent structures of liquids and liquid crystals. Unlike other books on the market, this comprehensive text not only deals with the primary fundamental ideas of statistical mechanics but also covers contemporary topics in this broad and rapidly developing area of chemistry and materials science.

This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker-Planck equations (H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed.Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details.Recent research on the integro-differential Fokker-Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems.

Thermodynamics and information touch theory every facet of chemistry. However, the physical chemistry curriculum digested by students worldwide is still heavily skewed toward heat/work principles established more than a century ago. Rectifying this situation, Chemical Thermodynamics and Information Theory with Applications explores applications drawn from the intersection of thermodynamics and information theory-two mature and far-reaching fields. In an approach that intertwines information science and chemistry, this book covers: The informational aspects of thermodynamic state equations The algorithmic aspects of transformations-compression, expansion, cyclic, and more The principles of best-practice programming How molecules transmit and modify information via collisions and chemical reactions Using examples from physical and organic chemistry, this book demonstrates how the disciplines of thermodynamics and information theory are intertwined. Accessible to curiosity-driven chemists with knowledge of basic calculus, probability, and statistics, the book provides a fresh perspective on time-honored subjects such as state transformations, heat and work exchanges, and chemical reactions.

This book is the fifth volume of papers on advanced problems of phase transitions and critical phenomena, the first four volumes appeared in 2004, 2007, 2012, and 2015. It aims to compile reviews in those aspects of criticality and related subjects that are of current interest. The seven 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 the first four 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 subject.

Der Grundkurs Theoretische Physik deckt in 7 Banden alle fur das Diplom und fur Bachelor/Master-Studiengange massgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester notwendige theoretisch-physikalische Rustzeug. UEbungsaufgaben mit ausfuhrlichen Loesungen dienen der Vertiefung des Stoffs. Der 6. Band zur Statistischen Physik wurde fur die Neuauflage grundlegend uberarbeitet und um aktuelle Entwicklungen erganzt. Durch die zweifarbige Gestaltung ist der Stoff jetzt noch ubersichtlicher gegliedert.

Ecosystems, the human brain, ant colonies, and economic networks are all complex systems displaying collective behaviour, or emergence, beyond the sum of their parts. Complexity science is the systematic investigation of these emergent phenomena, and stretches across disciplines, from physics and mathematics, to biological and social sciences. This introductory textbook provides detailed coverage of this rapidly growing field, accommodating readers from a variety of backgrounds, and with varying levels of mathematical skill. Part I presents the underlying principles of complexity science, to ensure students have a solid understanding of the conceptual framework. The second part introduces the key mathematical tools central to complexity science, gradually developing the mathematical formalism, with more advanced material provided in boxes. A broad range of end of chapter problems and extended projects offer opportunities for homework assignments and student research projects, with solutions available to instructors online. Key terms are highlighted in bold and listed in a glossary for easy reference, while annotated reading lists offer the option for extended reading and research.

This book highlights latest advancement in Mathematics, Physics and Chemistry. With the theme of "Innovative Science towards Sustainability and Industrial Revolution 4.0", ICFAS 2020 brings together leading experts, scientific communities and industrialists working in the field of applied sciences and mathematics from all over the world to share the most recent developments and cutting-edge discoveries addressing sustainability and industrial revolution 4.0 in the field. The conference topics include green materials, molecular modelling, catalysis, nanodevices and nanosystems, smart materials applications, solar cells technology, computational mathematics, data analysis and visualization, and numerical analysis. The contents of this book are useful for researchers, students, and industrial practitioners in the areas of Mathematics, Physics and Chemistry as most of the topics are in line with IR 4.0.

Flocks of birds, schools of fish and swarms of locusts display amazing forms of collective motion, while huge numbers of glow worms can emit light signals with almost unbelievable synchronization. These and many other collective phenomena in animal societies take place according to laws very similar to those governing the collective behavior in the inanimate nature, such as the magnetization of iron and the light radiation of lasers. During recent years, this has led to the study of swarm behavior as a challenging new field of science, in which ideas from the physical world are applied in order to understand the formation and structure of animal swarms. From these studies, it has become clear that such collective behavior of animals emerges in a self-organized way, without any need of overall coordination. In this book, we present different swarm phenomena of the animal world and compare them to their counterparts in physics, in a conceptual and non-technical way, addressed to a general readership.

Application of New Cybernetics in Physics describes the application of new cybernetics to physical problems and the resolution of basic physical paradoxes by considering external observer influence. This aids the reader in solving problems that were solved incorrectly or have not been solved. Three groups of problems of the new cybernetics are considered in the book: (a) Systems that can be calculated based on known physics of subsystems. This includes the external observer influence calculated from basic physical laws (ideal dynamics) and dynamics of a physical system influenced even by low noise (observable dynamics). (b) Emergent systems. This includes external noise from the observer by using the black box model (complex dynamics), external noise from the observer by using the observer's intuition (unpredictable dynamics), defining boundaries of application of scientific methods for system behavior prediction, and the role of the observer's intuition for unpredictable systems. (c) Methods for solution of basic physical paradoxes by using methods of the new cybernetics: the entropy increase paradox, Schroedinger's cat paradox (wave package reduction in quantum mechanics), the black holes information paradox, and the time wormholes grandfather paradox. All of the above paradoxes have the same resolution based on the principles of new cybernetics. Indeed, even a small interaction of an observer with an observed system results in their time arrows' alignment (synchronization) and results in the paradox resolution and appearance of the universal time arrow.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.