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97 results in Statistical Physics

Page 1 of 5

From Quantum Fields to Spin Glasses
  • Seminal Contributions of Giorgio Parisi to Theoretical Physics
  • Edited by Roberto Aloisio, Maria Chiara Angelini, Marco Bonvini, Giacomo Gradenigo, Enzo Marinari, Antonio Davide Polosa, Federico Ricci-Tersenghi
  • Coming soon
  • Expected online publication date:
    November 2026
    Print publication:
    30 November 2026
  • This book comprises a unique collection of insights into Nobel laureate Giorgio Parisi's groundbreaking work across physics, ranging from high-energy physics and spin glasses to turbulence and collective animal behaviour. Originating from a series of seminars at the Sapienza University of Rome, each chapter focuses on one of Parisi's seminal contributions, penned by leading experts who highlight the depth and interdisciplinary impact of his ideas. The volume revisits widely disseminated achievements like the Altarelli-Parisi equations and replica symmetry breaking, and presents lesser-known work, revealing hidden connections between seemingly distant domains. Enhanced by lively discussions and a personal retrospective from Parisi himself, this book is both a tribute to a visionary scientist and an invitation to discover the unifying threads woven throughout modern physics. Showcasing how one thinker's creativity can reshape entire landscapes of knowledge, it is invaluable for experienced researchers and motivated graduate students in the field of theoretical physics.

A Course in Interacting Particle Systems
  • Jan M. Swart
  • Coming soon
  • Expected online publication date:
    August 2026
    Print publication:
    31 August 2026
  • The culmination of years of teaching experience, this book provides a modern introduction to the mathematical theory of interacting particle systems. Assuming a background in probability and measure theory, it has been designed to support a one-semester course at a Master or Ph.D. level. It also provides a useful reference for researchers, containing several results that have not appeared in print in this form before. An emphasis is placed on graphical representations, which are used to give a construction that is intuitively easier to grasp than the traditional generator approach. Also included is an extensive look at duality theory, along with discussions of mean-field methods, phase transitions and critical behaviour. The text is illustrated with the results of numerical simulations and features exercises in every chapter. The theory is demonstrated on a range of models, reflecting the modern state of the subject and highlighting the scope of possible applications.

Networks
  • Probability and Statistics
  • A. D. Barbour, Gesine Reinert
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    30 June 2026
  • From social networks to biological systems, networks are a fundamental part of modern life. Network analysis is increasingly popular across the mathematical, physical, life and social sciences, offering insights into a range of phenomena, from developing new drugs based on intracellular interactions, to understanding the influence of social interactions on behaviour patterns. This book provides a toolkit for analyzing random networks, together with theoretical justification of the methods proposed. It combines methods from both probability and statistics, teaching how to build and analyze plausible models for random networks, and how to validate such models, to detect unusual features in the data, and to make predictions. Theoretical results are motivated by applications across a range of fields, and classical data sets are used for illustration throughout the book. This book offers a comprehensive introduction to the field for graduate students and researchers.

Universal Biology
  • The Physics of Life through the Macro-Micro Consistency Principle
  • Kunihiko Kaneko
  • Published online:
    11 November 2025
    Print publication:
    20 November 2025
  • Living systems consist of diverse components and constitute a hierarchy, from molecules to cells to organisms, which adapt to external perturbations and reproduce stably. This book describes the statistical and physical principles governing cell growth and reproduction, and the mechanisms for adaptation through noise, kinetic memory, and robust cell differentiation through cell to cell interaction and epigenetics. The laws governing rate, direction, and constraints of phenotypic evolution are examined from the perspective of microscopic units (molecules) and macroscopic states (cells), with a focus on maintaining consistency between these length and temporal scales. By integrating theoretical, computational, and experimental approaches, this book offers novel insights into biology from a physicist's perspective and provides a detailed picture of the universal characteristics of living systems. It is indispensable for students and researchers in physics, biology and mathematics interested in understanding the nature of life and the physical principles it is based upon.

Statistical Mechanics for Physicists and Mathematicians
  • Fabien Paillusson
  • Published online:
    28 July 2025
    Print publication:
    14 August 2025
  • Statistical mechanics employs the power of probability theory to shine a light upon the invisible world of matter's fundamental constituents, allowing us to accurately model the macroscopic physical properties of large ensembles of microscopic particles. This book delves into the conceptual and mathematical foundations of statistical mechanics to enhance understanding of complex physical systems and thermodynamic phenomena, whilst also providing a solid mathematical basis for further study and research in this important field. Readers will embark on a journey through important historical experiments in statistical physics and thermodynamics, exploring their intersection with modern applications, such as the thermodynamics of stars and the entropy associated with the mixing of two substances. An invaluable resource for students and researchers in physics and mathematics, this text provides numerous worked examples and exercises with full solutions, reinforcing key theoretical concepts and offering readers deeper insight into how these powerful tools are applied.

Nonequilibrium Statistical Physics
  • A Modern Perspective
  • 2nd edition
  • Roberto Livi, Paolo Politi
  • Published online:
    19 June 2025
    Print publication:
    03 July 2025
  • Statistical mechanics is hugely successful when applied to physical systems at thermodynamic equilibrium; however, most natural phenomena occur in nonequilibrium conditions and more sophisticated techniques are required to address this increased complexity. This second edition presents a comprehensive overview of nonequilibrium statistical physics, covering essential topics such as Langevin equations, Lévy processes, fluctuation relations, transport theory, directed percolation, kinetic roughening, and pattern formation. The first part of the book introduces the underlying theory of nonequilibrium physics, the second part develops key aspects of nonequilibrium phase transitions, and the final part covers modern applications. A pedagogical approach has been adopted for the benefit of graduate students and instructors, with clear language and detailed figures used to explain the relevant models and experimental results. With the inclusion of original material and organizational changes throughout the book, this updated edition will be an essential guide for graduate students and researchers in nonequilibrium thermodynamics.

Stochastic Thermodynamics
  • Udo Seifert
  • Published online:
    09 June 2025
    Print publication:
    19 June 2025
  • Stochastic thermodynamics has emerged as a comprehensive theoretical framework for a large class of non-equilibrium systems including molecular motors, biochemical reaction networks, colloidal particles in time-dependent laser traps, and bio-polymers under external forces. This book introduces the topic in a systematic way, beginning with a dynamical perspective on equilibrium statistical physics. Key concepts like the identification of work, heat and entropy production along individual stochastic trajectories are then developed and shown to obey various fluctuation relations beyond the well-established linear response regime. Representative applications are then discussed, including simple models of molecular motors, small chemical reaction networks, active particles, stochastic heat engines and information machines involving Maxwell demons. This book is ideal for graduate students and researchers of physics, biophysics, and physical chemistry, with an interest in non-equilibrium phenomena.

Working with Network Data
  • A Data Science Perspective
  • James Bagrow, Yong‐Yeol Ahn
  • Published online:
    06 June 2024
    Print publication:
    13 June 2024
  • Drawing examples from real-world networks, this essential book traces the methods behind network analysis and explains how network data is first gathered, then processed and interpreted. The text will equip you with a toolbox of diverse methods and data modelling approaches, allowing you to quickly start making your own calculations on a huge variety of networked systems. This book sets you up to succeed, addressing the questions of what you need to know and what to do with it, when beginning to work with network data. The hands-on approach adopted throughout means that beginners quickly become capable practitioners, guided by a wealth of interesting examples that demonstrate key concepts. Exercises using real-world data extend and deepen your understanding, and develop effective working patterns in network calculations and analysis. Suitable for both graduate students and researchers across a range of disciplines, this novel text provides a fast-track to network data expertise.

Tangles
  • A Structural Approach to Artificial Intelligence in the Empirical Sciences
  • Reinhard Diestel
  • Published online:
    16 May 2024
    Print publication:
    23 May 2024
  • Tangles offer a precise way to identify structure in imprecise data. By grouping qualities that often occur together, they not only reveal clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or of proteins. Tangles offer a new, structural, approach to artificial intelligence that can help us understand, classify, and predict complex phenomena.This has become possible by the recent axiomatization of the mathematical theory of tangles, which has made it applicable far beyond its origin in graph theory: from clustering in data science and machine learning to predicting customer behaviour in economics; from DNA sequencing and drug development to text and image analysis. Such applications are explored here for the first time. Assuming only basic undergraduate mathematics, the theory of tangles and its potential implications are made accessible to scientists, computer scientists, and social scientists.

The Physics of Flocking
  • Birth, Death, and Flight in Active Matter
  • John Toner
  • Published online:
    16 May 2024
    Print publication:
    23 May 2024
  • In creatures ranging from birds to fish to wildebeest, we observe the collective and coherent motion of large numbers of organisms, known as 'flocking.' John Toner, one of the founders of the field of active matter, uses the hydrodynamic theory of flocking to explain why a crowd of people can all walk, but not point, in the same direction. Assuming a basic undergraduate-level understanding of statistical mechanics, the text introduces readers to dry active matter and describes the current status of this rapidly developing field. Through the application of powerful techniques from theoretical condensed matter physics, such as hydrodynamic theories, the gradient expansion, and the renormalization group, readers are given the knowledge and tools to explore and understand this exciting field of research. This book will be valuable to graduate students and researchers in physics, mathematics, and biology with an interest in the hydrodynamic theory of flocking.

Density Matrix and Tensor Network Renormalization
  • Tao Xiang
  • Published online:
    18 January 2024
    Print publication:
    31 August 2023
  • Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.

Data Science for Complex Systems
  • Anindya S. Chakrabarti, K. Shuvo Bakar, Anirban Chakraborti
  • Published online:
    11 May 2023
    Print publication:
    25 May 2023
  • Many real-life systems are dynamic, evolving, and intertwined. Examples of such systems displaying 'complexity', can be found in a wide variety of contexts ranging from economics to biology, to the environmental and physical sciences. The study of complex systems involves analysis and interpretation of vast quantities of data, which necessitates the application of many classical and modern tools and techniques from statistics, network science, machine learning, and agent-based modelling. Drawing from the latest research, this self-contained and pedagogical text describes some of the most important and widely used methods, emphasising both empirical and theoretical approaches. More broadly, this book provides an accessible guide to a data-driven toolkit for scientists, engineers, and social scientists who require effective analysis of large quantities of data, whether that be related to social networks, financial markets, economies or other types of complex systems.

Network Science in Archaeology
  • Tom Brughmans, Matthew A. Peeples
  • Published online:
    06 April 2023
    Print publication:
    13 April 2023
  • The Cambridge Manual to Archaeological Network Science provides the first comprehensive guide to a field of research that has firmly established itself within archaeological practice in recent years. Network science methods are commonly used to explore big archaeological datasets and are essential for the formal study of past relational phenomena: social networks, transport systems, communication, and exchange. The volume offers a step-by-step description of network science methods and explores its theoretical foundations and applications in archaeological research, which are elaborately illustrated with archaeological examples. It also covers a vast range of network science techniques that can enhance archaeological research, including network data collection and management, exploratory network analysis, sampling issues and sensitivity analysis, spatial networks, and network visualisation. An essential reference handbook for both beginning and experienced archaeological network researchers, the volume includes boxes with definitions, boxed examples, exercises, and online supplementary learning and teaching materials.

Network Models for Data Science
  • Theory, Algorithms, and Applications
  • Alan Julian Izenman
  • Published online:
    22 March 2023
    Print publication:
    05 January 2023
  • This text on the theory and applications of network science is aimed at beginning graduate students in statistics, data science, computer science, machine learning, and mathematics, as well as advanced students in business, computational biology, physics, social science, and engineering working with large, complex relational data sets. It provides an exciting array of analysis tools, including probability models, graph theory, and computational algorithms, exposing students to ways of thinking about types of data that are different from typical statistical data. Concepts are demonstrated in the context of real applications, such as relationships between financial institutions, between genes or proteins, between neurons in the brain, and between terrorist groups. Methods and models described in detail include random graph models, percolation processes, methods for sampling from huge networks, network partitioning, and community detection. In addition to static networks the book introduces dynamic networks such as epidemics, where time is an important component.

A Complex Systems Approach to Epilepsy
  • Concept, Practice, and Therapy
  • Edited by Rod C. Scott, J. Matthew Mahoney
  • Published online:
    06 January 2023
    Print publication:
    26 January 2023
  • The epilepsies are devastating neurological disorders for which progress developing effective new therapies has slowed over recent decades, primarily due to the complexity of the brain at all scales. This reality has shifted the focus of experimental and clinical practice toward complex systems approaches to overcoming current barriers. Organized by scale from genes to whole brain, the chapters of this book survey the theoretical underpinnings and use of network and dynamical systems approaches to interpreting and modeling experimental and clinical data in epilepsy. The emphasis throughout is on the value of the non-trivial, and often counterintuitive, properties of complex systems, and how to leverage these properties to elaborate mechanisms of epilepsy and develop new therapies. In this essential book, readers will learn key concepts of complex systems theory applied across multiple scales and how each of these scales connects to epilepsy.

Complexity Science
  • The Study of Emergence
  • Henrik Jeldtoft Jensen
  • Published online:
    13 December 2022
    Print publication:
    17 November 2022
  • 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.

The Statistical Mechanics of Irreversible Phenomena
  • Pierre Gaspard
  • Published online:
    14 July 2022
    Print publication:
    28 July 2022
  • This book provides a comprehensive and self-contained overview of recent progress in nonequilibrium statistical mechanics, in particular, the discovery of fluctuation relations and other time-reversal symmetry relations. The significance of these advances is that nonequilibrium statistical physics is no longer restricted to the linear regimes close to equilibrium, but extends to fully nonlinear regimes. These important new results have inspired the development of a unifying framework for describing both the microscopic dynamics of collections of particles, and the macroscopic hydrodynamics and thermodynamics of matter itself. The book discusses the significance of this theoretical framework in relation to a broad range of nonequilibrium processes, from the nanoscale to the macroscale, and is essential reading for researchers and graduate students in statistical physics, theoretical chemistry and biological physics.

The Principles of Deep Learning Theory
  • An Effective Theory Approach to Understanding Neural Networks
  • Daniel A. Roberts, Sho Yaida
  • With contributions by Boris Hanin
  • Published online:
    05 May 2022
    Print publication:
    26 May 2022
  • This textbook establishes a theoretical framework for understanding deep learning models of practical relevance. With an approach that borrows from theoretical physics, Roberts and Yaida provide clear and pedagogical explanations of how realistic deep neural networks actually work. To make results from the theoretical forefront accessible, the authors eschew the subject's traditional emphasis on intimidating formality without sacrificing accuracy. Straightforward and approachable, this volume balances detailed first-principle derivations of novel results with insight and intuition for theorists and practitioners alike. This self-contained textbook is ideal for students and researchers interested in artificial intelligence with minimal prerequisites of linear algebra, calculus, and informal probability theory, and it can easily fill a semester-long course on deep learning theory. For the first time, the exciting practical advances in modern artificial intelligence capabilities can be matched with a set of effective principles, providing a timeless blueprint for theoretical research in deep learning.

The Mathematics of Finite Networks
  • An Introduction to Operator Graph Theory
  • Michael Rudolph
  • Published online:
    30 April 2022
    Print publication:
    12 May 2022
  • Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to understand the potential applications of operator graph theory.

The Statistical Physics of Data Assimilation and Machine Learning
  • Henry D. I. Abarbanel
  • Published online:
    27 January 2022
    Print publication:
    17 February 2022
  • Data assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics.

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