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Statistical mechanics is the third pillar of modern physics, next to quantum theory and relativity theory. It aims to account for the behaviour of macroscopic systems in terms of the dynamical laws that govern their microscopic constituents and probabilistic assumptions about them. In this Element, the authors investigate the philosophical and foundational issues that arise in SM. The authors introduce the two main theoretical approaches in SM, Boltzmannian SM and Gibbsian SM, and discuss how they conceptualise equilibrium and explain the approach to it. In doing so, the authors examine how probabilities are introduced into the theories, how they deal with irreversibility, how they understand the relation between the micro and the macro level, and how the two approaches relate to each other. Throughout, the authors also pinpoint open problems that can be subject of future research. This title is also available as Open Access on Cambridge Core.

Statistical mechanics.

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Entropy Beyond the Second Law presents a coherent formulation of all aspects of thermodynamics and statistical mechanics with entropy as the unifying theme. This second edition includes the novel entropic treatment of Bose-Einstein condensation, superfluidity, and high temperature superconductivity. The new physical insights and the quantitative agreement with experimental measurement provide concrete examples of the universal approach based on entropy advocated in the book. Thermodynamics and statistical mechanics are important subjects, and students, academics, and researchers require the fundamental concepts to be clearly and concisely presented, as part of a unified whole, and the mathematical derivations to be explained with detailed physical explanation and applications.

Entropy. --- Thermodynamics. --- Statistical mechanics. --- Thermodynamics & heat. --- SCIENCE / Mechanics / Thermodynamics.

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This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.

C*-algebras. --- Quantum statistics. --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics --- Mathematical physics. --- Statistical Mechanics. --- Quantum physics. --- Functional analysis. --- Mathematical Physics. --- Mathematical Methods in Physics. --- Quantum Physics. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Physical mathematics --- Mathematics --- Estadística quàntica --- C*-àlgebres --- Statistical mechanics. --- Quantum theory.

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Condensed matter. --- Mathematical physics. --- Statistical mechanics. --- Physical mathematics --- Physics --- Mathematics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics

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This book highlights the fundamentals for understanding the essential problems and latest progresses in basic water science. Water is the most abundant, fundamental and important matter in nature. Arguably it is also the material that human beings study the most but misunderstand the most. Compared with the environmental science and engineering research activities on water resources, water pollution and water usage closely related to social problems at the macro level, basic scientific research on water at the molecular level has just emerged, the impact of which is not fully recognized yet. This book is devoted to introducing some important advances in the field of basic water science in past decades, with a particular emphasis on recent results on water and the interactions between water and solid surfaces at the molecular level. Starting from introducing concepts and popular theoretical and experimental methods for basic water research, this book mainly focuses on the atomic composition, electronic structure, and physicochemical properties of water molecules, water clusters and water layers (including surface water layers and water surface layers), rules for water adsorption on metals, oxides, and other typical solid surfaces such as salt, as well as the microscopic processes and mechanisms of water diffusion, wetting, decomposition and phase transformations under a variety of conditions. It is a good reference book for students and researchers in water-related science.

Hydrology. --- Water. --- Hydrology --- Aquatic sciences --- Earth sciences --- Hydrography --- Water --- Atomic structure . --- Molecular structure. --- Surfaces (Physics). --- Microclusters. --- Condensed matter. --- Quantum physics. --- Quantum statistics. --- Atomic and Molecular Structure and Properties. --- Surface and Interface and Thin Film. --- Atomic and Molecular Clusters. --- Phase Transition and Critical Phenomena. --- Atom and Molecule Optics and Interferometry. --- Quantum Gases and Condensates. --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Atomic clusters --- Clusters, Atomic --- Clusters, Molecular --- Microcluster physics --- Molecular clusters --- Atoms --- Microphysics --- Surface chemistry --- Surfaces (Technology) --- Structure, Molecular --- Chemical structure --- Structural bioinformatics --- Structure, Atomic --- Atomic theory --- Atomic structure. --- Surfaces (Physics) --- Quantum theory.