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Statistical physics --- $ Bose-Einstein statistics --- $ Quantum statistics --- $ Fermi-Dirac statistics --- $ Maxwell-Boltzmann distribution --- $ Statistical mechanics --- Thermodynamics --- 536.7 --- 531.19 --- Statistical mechanics --- #WSCH:MACB --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Mechanics, Analytic --- Quantum statistics --- Thermodynamics. Energetics --- 531.19 Statistical mechanics --- 536.7 Thermodynamics. Energetics
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Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.
Mathematical physics. --- Diffusion. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Gases --- Liquids --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Physical mathematics --- Diffusion --- Properties --- Mathematics --- Affine space. --- Algebra. --- Axiom. --- Bell's theorem. --- Brownian motion. --- Central limit theorem. --- Classical mathematics. --- Classical mechanics. --- Clifford algebra. --- Combinatorial proof. --- Commutative property. --- Constructive quantum field theory. --- Continuum hypothesis. --- David Hilbert. --- Dimension (vector space). --- Discrete mathematics. --- Distribution (mathematics). --- Eigenfunction. --- Equation. --- Euclidean space. --- Experimental mathematics. --- Fermi–Dirac statistics. --- Feynman–Kac formula. --- First-order logic. --- Fokker–Planck equation. --- Foundations of mathematics. --- Fractal dimension. --- Gaussian process. --- Girsanov theorem. --- Gödel's incompleteness theorems. --- Hilbert space. --- Hilbert's program. --- Holomorphic function. --- Infinitesimal. --- Integer. --- Internal set theory. --- Interval (mathematics). --- Limit (mathematics). --- Mathematical induction. --- Mathematical optimization. --- Mathematical proof. --- Mathematician. --- Mathematics. --- Measurable function. --- Measure (mathematics). --- Minkowski space. --- Natural number. --- Neo-Riemannian theory. --- Non-standard analysis. --- Number theory. --- Operator algebra. --- Ornstein–Uhlenbeck process. --- Orthonormal basis. --- Perturbation theory (quantum mechanics). --- Philosophy of mathematics. --- Predicate (mathematical logic). --- Probability measure. --- Probability space. --- Probability theory. --- Probability. --- Projection (linear algebra). --- Pure mathematics. --- Pythagorean theorem. --- Quantum field theory. --- Quantum fluctuation. --- Quantum gravity. --- Quantum harmonic oscillator. --- Quantum mechanics. --- Quantum system. --- Quantum teleportation. --- Random variable. --- Real number. --- Renormalization group. --- Renormalization. --- Riemann mapping theorem. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Schrödinger equation. --- Scientific notation. --- Set (mathematics). --- Sign (mathematics). --- Sobolev inequality. --- Special relativity. --- Spectral theorem. --- Spin (physics). --- Statistical mechanics. --- Stochastic calculus. --- Stochastic differential equation. --- Tensor algebra. --- Theorem. --- Theoretical physics. --- Theory. --- Turing machine. --- Variable (mathematics). --- Von Neumann algebra. --- Wiener process. --- Wightman axioms. --- Zermelo–Fraenkel set theory.
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About 120 years ago, James Clerk Maxwell introduced his now legendary hypothetical "demon" as a challenge to the integrity of the second law of thermodynamics. Fascination with the demon persisted throughout the development of statistical and quantum physics, information theory, and computer science--and linkages have been established between Maxwell's demon and each of these disciplines. The demon's seductive quality makes it appealing to physical scientists, engineers, computer scientists, biologists, psychologists, and historians and philosophers of science. Until now its important source material has been scattered throughout diverse journals.This book brings under one cover twenty-five reprints, including seminal works by Maxwell and William Thomson; historical reviews by Martin Klein, Edward Daub, and Peter Heimann; information theoretic contributions by Leo Szilard, Leon Brillouin, Dennis Gabor, and Jerome Rothstein; and innovations by Rolf Landauer and Charles Bennett illustrating linkages with the limits of computation. An introductory chapter summarizes the demon's life, from Maxwell's illustration of the second law's statistical nature to the most recent "exorcism" of the demon based on a need periodically to erase its memory. An annotated chronological bibliography is included.Originally published in 1990.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Thermodynamics. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Maxwell's demon. --- Adiabatic process. --- Automaton. --- Available energy (particle collision). --- Billiard-ball computer. --- Black hole information paradox. --- Black hole thermodynamics. --- Black-body radiation. --- Boltzmann's entropy formula. --- Boyle's law. --- Calculation. --- Carnot's theorem (thermodynamics). --- Catalysis. --- Chaos theory. --- Computation. --- Copying. --- Creation and annihilation operators. --- Digital physics. --- Dissipation. --- Distribution law. --- Domain wall. --- EPR paradox. --- Energy level. --- Entropy of mixing. --- Entropy. --- Exchange interaction. --- Expectation value (quantum mechanics). --- Extrapolation. --- Fair coin. --- Fermi–Dirac statistics. --- Gibbs free energy. --- Gibbs paradox. --- Guessing. --- Halting problem. --- Hamiltonian mechanics. --- Heat engine. --- Heat. --- Helmholtz free energy. --- Ideal gas. --- Idealization. --- Information theory. --- Instant. --- Internal energy. --- Irreversible process. --- James Prescott Joule. --- Johnson–Nyquist noise. --- Kinetic theory of gases. --- Laws of thermodynamics. --- Least squares. --- Loschmidt's paradox. --- Ludwig Boltzmann. --- Maxwell–Boltzmann distribution. --- Mean free path. --- Measurement. --- Mechanical equivalent of heat. --- Microscopic reversibility. --- Molecule. --- Negative temperature. --- Negentropy. --- Newton's law of universal gravitation. --- Nitrous oxide. --- Non-equilibrium thermodynamics. --- Old quantum theory. --- Particle in a box. --- Perpetual motion. --- Photon. --- Probability. --- Quantity. --- Quantum limit. --- Quantum mechanics. --- Rectangular potential barrier. --- Result. --- Reversible computing. --- Reversible process (thermodynamics). --- Richard Feynman. --- Rolf Landauer. --- Rudolf Clausius. --- Scattering. --- Schrödinger equation. --- Second law of thermodynamics. --- Self-information. --- Spontaneous process. --- Standard state. --- Statistical mechanics. --- Superselection. --- Temperature. --- Theory of heat. --- Theory. --- Thermally isolated system. --- Thermodynamic equilibrium. --- Thermodynamic system. --- Thought experiment. --- Turing machine. --- Ultimate fate of the universe. --- Uncertainty principle. --- Unitarity (physics). --- Van der Waals force. --- Wave function collapse. --- Work output.
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