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Potts Models and Related Problems in Statistical Mechanics
This unique volume aims to provide a first comprehensive assessment on attributes, conditions and characters which constitute a liveable city. The book posits that the degree of liveability depends on five themes: satisfaction with the freedom from want; satisfaction with the state of the natural environment and its management; satisfaction with freedom from fear; satisfaction with the socio-cultural conditions; and satisfaction with public governance.The authors attempt to be more constructive through performing policy simulations by first identifying relative weaknesses and strengths of 64 global cities across major continents including European, Asian, Middle Eastern, North and South American cities. The book also ranks and simulates 36 Asian cities separately, of which many are emerging third-world cities that are in need of policy guidance.
This volume is a collection of original papers and reviews in honour of James McGuire, one of the pioneers of integrable models in statistical physics. The broad range of articles offers a timely perspective on the current status of statistical mechanics, identifying both recent results as well as future challenges. The work contains a number of overviews of standard topics such as exactly solved lattice models and their various applications in statistical physics, from models of strongly correlated electrons to the conformational properties of polymer chains. It is equally wide ranging in its coverage of new directions and developing fields including quantum computers, financial markets, chaotic systems, Feigenbaum scaling, proteins, brain behaviour, immunology, Markov superposition, Bose-Einstein condensation, random matrices, exclusion statistics, vertex operator algebras and D-unsolvability.The level of coverage is appropriate for graduate students. It will be equally of interest to professional physicists who want to learn about progress in statistical physics in recent years. Experts will find this work useful because of its broad sweep of topics and its discussion of remaining unsolved problems.
The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood–Richardson rule and the Schur–Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.
The purpose of this textbook is to bring together, in a self-contained introductory form, the scattered material in the field of stochastic processes and statistical physics. It offers the opportunity of being acquainted with stochastic, kinetic and nonequilibrium processes. Although the research techniques in these areas have become standard procedures, they are not usually taught in the normal courses on statistical physics. For students of physics in their last year and graduate students who wish to gain an invaluable introduction on the above subjects, this book is a necessary tool. Contents:Stochastic Processes and the Master Equation:Stochastic ProcessesMarkovian ProcessesMaster EquationsKramers Moyal ExpansionBrownian Motion, Langevin and Fokker-Planck EquationsDistributions, BBGKY Hierarchy, Density Operator:Probability Density as a FluidBBGKY HierarchyMicroscopic Balance EquationsDensity OperatorLinear Nonequilibrium Thermodynamics and Onsager Relations:Onsager Regression to Equilibrium HypothesisOnsager RelationsMinimum Production of EntropyLinear Response Theory, Fluctuation-Dissipation Theorem:Correlation Functions: Definitions and PropertiesLinear Response TheoryFluctuation-Dissipation TheoremInstabilities and Far from Equilibrium Phase-Transitions:Limit Cycles, Bifurcations, Symmetry BreakingNoise Induced TransitionsFormation and Propagation of Patterns in Far from Equilibrium Systems:Reaction-Diffusion Descriptions and Pattern FormationPattern Propagation Readership: Graduate students in physics and chemistry. keywords:Stochastic Processes;Langevin and Fokker-Planck Equations;Statistical Physics;Onsager Relations;Linear Response;Nonequilibrium Statistical Physics;Transport Processes;Noise Induced Transitions;Instabilities;Pattern Formation and Propagation “This book introduces ways to investigate nonequilibrium statistical physics, mainly via stochastic processes, and presents results achieved with such methodology … it is suitable for seminars directed towards relatively mature students in theoretical physics or applied mathematics.” H Muthsam “The present book is a good choice for a single book covering the field … suitable for undergraduate students in the last year and graduate students. They will find in it a suggestive introduction that motivates them to dig deeper into the field and to look for those topics omitted from the text … highly recommended to anyone interested in becoming acquainted with nonequilibrium statistical physics.” Journal of Statistical Physics
This book aims at guiding the reader with continuity from the elements of classical equilibrium thermodynamics to the formal problems of global non equilibrium thermodynamics necessary to describe an ?active system? such is a thermodynamic ecosystem. To this purpose, the brief review of equilibrium thermodynamics emphasizes the concepts of disequilibrium, Carnot cycles and less efficient cycles, and Gibbs availability as the distance from equilibrium. In this way the reader is taken by hand to accept the concept of Gibbs efficiency of the ecosystem Earth as a property given to us by the cosmological evolution. The final chapters are devoted to the optimal control theory of global non-equilibrium systems. An elementary theory of zero energy thermodynamic automata is presented. A thermodynamic automation with four temperatures and three controls is discussed in detail.

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