Oliver Penrose
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199231256
- eISBN:
- 9780191710803
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199231256.003.0015
- Subject:
- Mathematics, History of Mathematics
Kelvin played a big part in the development of statistical mechanics, both for equilibrium and non-equilibrium. This chapter reviews these developments, taking a particular interest in Kelvin's own ...
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Kelvin played a big part in the development of statistical mechanics, both for equilibrium and non-equilibrium. This chapter reviews these developments, taking a particular interest in Kelvin's own contributions. Topics covered include Kelvin and thermoelectricity, gas modeled as a collection of molecules, the reversibility paradox, mathematical probability models, and Boltzmann's equations.Less
Kelvin played a big part in the development of statistical mechanics, both for equilibrium and non-equilibrium. This chapter reviews these developments, taking a particular interest in Kelvin's own contributions. Topics covered include Kelvin and thermoelectricity, gas modeled as a collection of molecules, the reversibility paradox, mathematical probability models, and Boltzmann's equations.
Walter T. Grandy, Jr.
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199546176
- eISBN:
- 9780191720161
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546176.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The ...
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This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.Less
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.
CARLO CERCIGNANI
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570646
- eISBN:
- 9780191717949
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570646.003.0007
- Subject:
- Physics, History of Physics
This chapter discusses equilibrium statistical mechanics for systems more complicated than monatomic gases, as well as the problem of the trend towards equilibrium of these systems. Ludwig Boltzmann ...
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This chapter discusses equilibrium statistical mechanics for systems more complicated than monatomic gases, as well as the problem of the trend towards equilibrium of these systems. Ludwig Boltzmann is credited for having begun this branch of statistical mechanics with a basic paper written in 1884, in which he formulated the hypothesis that some among the possible steady distributions can be interpreted as macroscopic equilibrium states. This fundamental work by Boltzmann was taken up again, widened, and expounded in a classical treatise by Josiah Willard Gibbs. In his paper, Boltzmann described statistical families of steady distributions, which he called orthodes. Boltzmann showed that there are at least two ensembles of this kind, the ergode (Gibbs's microcanonical ensemble) and the holode (Gibbs's canonical ensemble). This article also explains why statistical mechanics is usually attributed to Gibbs and not to Boltzmann, the problem of trend to equilibrium and ergodic theory, and Max Planck's work on statistical mechanics.Less
This chapter discusses equilibrium statistical mechanics for systems more complicated than monatomic gases, as well as the problem of the trend towards equilibrium of these systems. Ludwig Boltzmann is credited for having begun this branch of statistical mechanics with a basic paper written in 1884, in which he formulated the hypothesis that some among the possible steady distributions can be interpreted as macroscopic equilibrium states. This fundamental work by Boltzmann was taken up again, widened, and expounded in a classical treatise by Josiah Willard Gibbs. In his paper, Boltzmann described statistical families of steady distributions, which he called orthodes. Boltzmann showed that there are at least two ensembles of this kind, the ergode (Gibbs's microcanonical ensemble) and the holode (Gibbs's canonical ensemble). This article also explains why statistical mechanics is usually attributed to Gibbs and not to Boltzmann, the problem of trend to equilibrium and ergodic theory, and Max Planck's work on statistical mechanics.
David Wallace
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199546961
- eISBN:
- 9780191741418
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546961.003.0012
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
quantum-mechanical branching is a time-directed process, while the underlying equations of quantum theory admit no preferred direction of time. The chapter demonstrates that this apparent ...
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quantum-mechanical branching is a time-directed process, while the underlying equations of quantum theory admit no preferred direction of time. The chapter demonstrates that this apparent incompatibility is an aspect of the better-known apparent incompatibility between the directedness in time of statistical mechanics and the underlying time-symmeric microphysics. The chapter sketches a unified way of resolving this apparent incompatibility, related to but distinct from the currently-popular idea of a ‘past hypothesis’.Less
quantum-mechanical branching is a time-directed process, while the underlying equations of quantum theory admit no preferred direction of time. The chapter demonstrates that this apparent incompatibility is an aspect of the better-known apparent incompatibility between the directedness in time of statistical mechanics and the underlying time-symmeric microphysics. The chapter sketches a unified way of resolving this apparent incompatibility, related to but distinct from the currently-popular idea of a ‘past hypothesis’.
Craig Callender
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199577439
- eISBN:
- 9780191730603
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577439.003.0004
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
This chapter unfolds a central philosophical problem of statistical mechanics. This problem lies in a clash between the Static Probabilities offered by statistical mechanics and the Dynamic ...
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This chapter unfolds a central philosophical problem of statistical mechanics. This problem lies in a clash between the Static Probabilities offered by statistical mechanics and the Dynamic Probabilities provided by classical or quantum mechanics. The chapter looks at the Boltzmann and Gibbs approaches in statistical mechanics and construes some of the great controversies in the field — for instance the Reversibility Paradox — as instances of this conflict. It furthermore argues that a response to this conflict is a critical choice that shapes one's understanding of statistical mechanics itself, namely, whether it is to be conceived as a special or fundamental science. The chapter details some of the pitfalls of the latter ‘globalist’ position and seeks defensible ground for a kind of ‘localist’ alternative.Less
This chapter unfolds a central philosophical problem of statistical mechanics. This problem lies in a clash between the Static Probabilities offered by statistical mechanics and the Dynamic Probabilities provided by classical or quantum mechanics. The chapter looks at the Boltzmann and Gibbs approaches in statistical mechanics and construes some of the great controversies in the field — for instance the Reversibility Paradox — as instances of this conflict. It furthermore argues that a response to this conflict is a critical choice that shapes one's understanding of statistical mechanics itself, namely, whether it is to be conceived as a special or fundamental science. The chapter details some of the pitfalls of the latter ‘globalist’ position and seeks defensible ground for a kind of ‘localist’ alternative.
Stephen J. Blundell and Katherine M. Blundell
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
An understanding of thermal physics is crucial to much of modern physics, chemistry, and engineering. This book provides a modern introduction to the main principles that are foundational to thermal ...
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An understanding of thermal physics is crucial to much of modern physics, chemistry, and engineering. This book provides a modern introduction to the main principles that are foundational to thermal physics, thermodynamics, and statistical mechanics. The key concepts are carefully presented in a clear way, and new ideas are illustrated with worked examples as well as a description of the historical background to their discovery. Applications are presented to subjects as diverse as stellar astrophysics, information and communication theory, condensed matter physics, and climate change. Each chapter concludes with detailed exercises. This second edition of the text maintains the structure and style of the first edition but extends its coverage of thermodynamics and statistical mechanics to include several new topics, including osmosis, diffusion problems, Bayes theorem, radiative transfer, the Ising model, and Monte Carlo methods. New examples and exercises have been added throughout.Less
An understanding of thermal physics is crucial to much of modern physics, chemistry, and engineering. This book provides a modern introduction to the main principles that are foundational to thermal physics, thermodynamics, and statistical mechanics. The key concepts are carefully presented in a clear way, and new ideas are illustrated with worked examples as well as a description of the historical background to their discovery. Applications are presented to subjects as diverse as stellar astrophysics, information and communication theory, condensed matter physics, and climate change. Each chapter concludes with detailed exercises. This second edition of the text maintains the structure and style of the first edition but extends its coverage of thermodynamics and statistical mechanics to include several new topics, including osmosis, diffusion problems, Bayes theorem, radiative transfer, the Ising model, and Monte Carlo methods. New examples and exercises have been added throughout.
Glenn H. Fredrickson
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198567295
- eISBN:
- 9780191717956
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567295.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and ...
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This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and operators for polymer segment density and stress are introduced. Analytical approximation schemes for solving the Fokker-Planck equations and evaluating operators are presented. Effective numerical methods are also described, with an emphasis on spectral collocation techniques.Less
This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and operators for polymer segment density and stress are introduced. Analytical approximation schemes for solving the Fokker-Planck equations and evaluating operators are presented. Effective numerical methods are also described, with an emphasis on spectral collocation techniques.
Nasr M. Ghoniem and Daniel D. Walgraef
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199298686
- eISBN:
- 9780191720222
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199298686.003.0010
- Subject:
- Physics, Condensed Matter Physics / Materials
Computational modelling of materials behaviour is becoming a reliable tool of scientific investigation, complementary to traditional theory and experimentation. The Multiscale Materials Modelling ...
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Computational modelling of materials behaviour is becoming a reliable tool of scientific investigation, complementary to traditional theory and experimentation. The Multiscale Materials Modelling (MMM) approach reflects the realization that continuum and atomistic analysis methods are complementary. This chapter describes the most popular numerical techniques of each component that make up the MMM paradigm for modelling nano- and micro-systems: Quantum Mechanics (QM), Molecular Dynamics (MD), Monte Carlo (MC), Dislocation Dynamics (DD), Statistical Mechanics (SM), and Continuum Mechanics (CM).Less
Computational modelling of materials behaviour is becoming a reliable tool of scientific investigation, complementary to traditional theory and experimentation. The Multiscale Materials Modelling (MMM) approach reflects the realization that continuum and atomistic analysis methods are complementary. This chapter describes the most popular numerical techniques of each component that make up the MMM paradigm for modelling nano- and micro-systems: Quantum Mechanics (QM), Molecular Dynamics (MD), Monte Carlo (MC), Dislocation Dynamics (DD), Statistical Mechanics (SM), and Continuum Mechanics (CM).
V. Jakšić, Y. Ogata, Y. Pautrat, and C.-A. Pillet
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199652495
- eISBN:
- 9780191741203
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652495.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter presents a self-contained introduction to some recent developments in nonequilibrium quantum statistical mechanics. In the elementary framework of finite dimensional quantum systems it ...
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This chapter presents a self-contained introduction to some recent developments in nonequilibrium quantum statistical mechanics. In the elementary framework of finite dimensional quantum systems it introduces the concept of entropy production and discusses various generating functionals which encode the statistical properties of its fluctuations. It explores the physical interpretations of these functionals and their mathematical properties. In particular, it investigates their relations to linear response theory, full counting statistics, and quantum hypothesis testing. The chapter discusses very briefly more technical issues linked to the thermodynamic limit as well as to the large time limit. These two limits turn the elementary, finite time fluctuation theory into a powerful machinery, which yields important information on the asymptotic behaviour of infinitely extended quantum systems, e.g., open systems coupled to infinite reservoirs. An essential mathematical tool to deal with such a system is Tomita–Takesaki's modular theory of von Neumann algebras. The power of this theory is somewhat shadowed by its technical aspects. Finite dimensional quantum systems are special since all the structures and results of this machinery can be described by elementary tools.Less
This chapter presents a self-contained introduction to some recent developments in nonequilibrium quantum statistical mechanics. In the elementary framework of finite dimensional quantum systems it introduces the concept of entropy production and discusses various generating functionals which encode the statistical properties of its fluctuations. It explores the physical interpretations of these functionals and their mathematical properties. In particular, it investigates their relations to linear response theory, full counting statistics, and quantum hypothesis testing. The chapter discusses very briefly more technical issues linked to the thermodynamic limit as well as to the large time limit. These two limits turn the elementary, finite time fluctuation theory into a powerful machinery, which yields important information on the asymptotic behaviour of infinitely extended quantum systems, e.g., open systems coupled to infinite reservoirs. An essential mathematical tool to deal with such a system is Tomita–Takesaki's modular theory of von Neumann algebras. The power of this theory is somewhat shadowed by its technical aspects. Finite dimensional quantum systems are special since all the structures and results of this machinery can be described by elementary tools.
John T. Roberts
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199557707
- eISBN:
- 9780191721052
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199557707.003.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
The idea that science has discovered that our universe is governed by laws of nature is arguably an important part of the modern scientific world‐view. The distinction between laws and other truths ...
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The idea that science has discovered that our universe is governed by laws of nature is arguably an important part of the modern scientific world‐view. The distinction between laws and other truths discovered by science is essential in at least some scientific reasoning, for example in statistical mechanics. The idea that laws of nature really govern the universe—and that they are not merely regularities that form an elegant system, as they are according to proponents of Humeanism (e.g. David Lewis)—turns out to play a crucial role in much scientific reasoning having to do with so‐called fine‐tuning. This chapter offers a formulation of the law‐governed world‐picture and outlines an argument for a new account of lawhood that vindicates that picture.Less
The idea that science has discovered that our universe is governed by laws of nature is arguably an important part of the modern scientific world‐view. The distinction between laws and other truths discovered by science is essential in at least some scientific reasoning, for example in statistical mechanics. The idea that laws of nature really govern the universe—and that they are not merely regularities that form an elegant system, as they are according to proponents of Humeanism (e.g. David Lewis)—turns out to play a crucial role in much scientific reasoning having to do with so‐called fine‐tuning. This chapter offers a formulation of the law‐governed world‐picture and outlines an argument for a new account of lawhood that vindicates that picture.
David Sherrington
Paul Goldbart and Nigel Goldenfeld (eds)
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
The collection of trails blazed by Sam Edwards during half a century of fundamental research in theoretical physics is truly astonishing. He led theoretical physics into uncharted territories from ...
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The collection of trails blazed by Sam Edwards during half a century of fundamental research in theoretical physics is truly astonishing. He led theoretical physics into uncharted territories from his roots in quantum field theory — beginning with his seminal work on the transport properties of disordered metals, and continuing to the present day with his ground-breaking efforts to create a statistical mechanics of granular materials. Along the way, he and his collaborators developed the first modern theory of polymers in solution and in the rubbery state; created and explored the tube concept, which has had momentous implications for understanding the viscoelasticity of polymer melts; formulated the spin-glass problem and provided its first solutions using the method of replicas — work that has had profound implications in areas as diverse as combinatorial optimization, neural networks, as well as glassy systems; made important contributions to the still-unsolved problem of Navier-Stokes turbulence; and initiated the recent explosion of activity in the dynamics of growing interfaces. This book celebrates Sam's impact by collecting together and reprinting eleven of his papers, each of which played a seminal role and started a new field of study, each followed by one or more original articles by experts in the relevant fields demonstrating how the topics Sam started have developed to the modern day.Less
The collection of trails blazed by Sam Edwards during half a century of fundamental research in theoretical physics is truly astonishing. He led theoretical physics into uncharted territories from his roots in quantum field theory — beginning with his seminal work on the transport properties of disordered metals, and continuing to the present day with his ground-breaking efforts to create a statistical mechanics of granular materials. Along the way, he and his collaborators developed the first modern theory of polymers in solution and in the rubbery state; created and explored the tube concept, which has had momentous implications for understanding the viscoelasticity of polymer melts; formulated the spin-glass problem and provided its first solutions using the method of replicas — work that has had profound implications in areas as diverse as combinatorial optimization, neural networks, as well as glassy systems; made important contributions to the still-unsolved problem of Navier-Stokes turbulence; and initiated the recent explosion of activity in the dynamics of growing interfaces. This book celebrates Sam's impact by collecting together and reprinting eleven of his papers, each of which played a seminal role and started a new field of study, each followed by one or more original articles by experts in the relevant fields demonstrating how the topics Sam started have developed to the modern day.
S. F. Edwards and R. B. S. Oakeshott
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.003.0024
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
There is increasing interest in applying the methods of statistical mechanics and of transport theory to systems which are neither atomistic, nor in equilibrium, but which still fulfill a remaining ...
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There is increasing interest in applying the methods of statistical mechanics and of transport theory to systems which are neither atomistic, nor in equilibrium, but which still fulfill a remaining tenet of statistical physics which is that systems can be completely defined by a very small number of parameters and can be constructed in a reproducible way. Powders fall into this category. This chapter sets up a framework for describing the state of the powder, basing the development on anologies with statistical mechanics. It is argued that powders have an entropy, but it will be the volume which plays the role of the energy in normal statistical mechanics: the energy corresponding to the powder's thermal temperature of 300 K is negligible. In statistical mechanics, the most fundamental entry is via the microcanonical ensemble. This is a closed system, contained in a volume V, which is assumed to take up all configurations subject to the Hamiltonian function taking the value E with equal probability.Less
There is increasing interest in applying the methods of statistical mechanics and of transport theory to systems which are neither atomistic, nor in equilibrium, but which still fulfill a remaining tenet of statistical physics which is that systems can be completely defined by a very small number of parameters and can be constructed in a reproducible way. Powders fall into this category. This chapter sets up a framework for describing the state of the powder, basing the development on anologies with statistical mechanics. It is argued that powders have an entropy, but it will be the volume which plays the role of the energy in normal statistical mechanics: the energy corresponding to the powder's thermal temperature of 300 K is negligible. In statistical mechanics, the most fundamental entry is via the microcanonical ensemble. This is a closed system, contained in a volume V, which is assumed to take up all configurations subject to the Hamiltonian function taking the value E with equal probability.
A. J. Leggett
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211241
- eISBN:
- 9780191706837
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211241.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses three fundamental questions which the majority of the physics community believes are not worthy of attention and a minority believes are crucial and in urgent need of ...
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This chapter discusses three fundamental questions which the majority of the physics community believes are not worthy of attention and a minority believes are crucial and in urgent need of attention. The first concerns the “anthropic principle”: to what extent is it an “explanation” of basic physical data, such as the dimensionality of space-time, the values of the fundamental constants, etc., to observe that were they appreciably different, human life and consciousness could not have evolved to the point of asking the question? The second has to do with the “arrow of time”: how is the everyday sense of the “flow” of time from past to future consistent with the invariance of the laws of physics under time reversal? The third problem is how to incorporate the occurrence of definite outcomes within the framework of quantum mechanics (the “quantum measurement problem”).Less
This chapter discusses three fundamental questions which the majority of the physics community believes are not worthy of attention and a minority believes are crucial and in urgent need of attention. The first concerns the “anthropic principle”: to what extent is it an “explanation” of basic physical data, such as the dimensionality of space-time, the values of the fundamental constants, etc., to observe that were they appreciably different, human life and consciousness could not have evolved to the point of asking the question? The second has to do with the “arrow of time”: how is the everyday sense of the “flow” of time from past to future consistent with the invariance of the laws of physics under time reversal? The third problem is how to incorporate the occurrence of definite outcomes within the framework of quantum mechanics (the “quantum measurement problem”).
Hidetoshi Nishimori
- Published in print:
- 2001
- Published Online:
- January 2010
- ISBN:
- 9780198509417
- eISBN:
- 9780191709081
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509417.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical ...
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Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical techniques have been developed to establish a theory of spin glasses. Surprisingly, these techniques have offered new tools and viewpoints for the understanding of information processing problems, including neural networks, error-correcting codes, image restoration, and optimization problems. A vast, interdisciplinary field has consequently been developing between physics and information, or more specifically, between the statistical physics of spin glasses and several important aspects of information processing tasks. This book provides a broad overview of this new field. It also contains detailed descriptions of the theory of spin glasses.Less
Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical techniques have been developed to establish a theory of spin glasses. Surprisingly, these techniques have offered new tools and viewpoints for the understanding of information processing problems, including neural networks, error-correcting codes, image restoration, and optimization problems. A vast, interdisciplinary field has consequently been developing between physics and information, or more specifically, between the statistical physics of spin glasses and several important aspects of information processing tasks. This book provides a broad overview of this new field. It also contains detailed descriptions of the theory of spin glasses.
D.A. Lavis
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199577439
- eISBN:
- 9780191730603
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577439.003.0003
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
This chapter defends and refines a specific objectivist interpretation of probabilities in statistical mechanics. For ergodic systems, probabilities are defined as time-averages. For other systems, ...
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This chapter defends and refines a specific objectivist interpretation of probabilities in statistical mechanics. For ergodic systems, probabilities are defined as time-averages. For other systems, ergodic decomposition is applied, and stochastic nomological machines are used to assign probabilities over the members of the decomposition. The relevance of this analysis to the Boltzmann and Gibbs approaches to statistical mechanics is discussed. The chapter shows that the proposed definition of probabilities matches a Boltzmann-like approach particularly well if the sharp distinction between equilibrium and non-equilibrium is given up and if more emphasis is laid upon the global time profile of entropy. The chapter furthermore argues that the alleged weaknesses of the time-average definition of probability are avoided.Less
This chapter defends and refines a specific objectivist interpretation of probabilities in statistical mechanics. For ergodic systems, probabilities are defined as time-averages. For other systems, ergodic decomposition is applied, and stochastic nomological machines are used to assign probabilities over the members of the decomposition. The relevance of this analysis to the Boltzmann and Gibbs approaches to statistical mechanics is discussed. The chapter shows that the proposed definition of probabilities matches a Boltzmann-like approach particularly well if the sharp distinction between equilibrium and non-equilibrium is given up and if more emphasis is laid upon the global time profile of entropy. The chapter furthermore argues that the alleged weaknesses of the time-average definition of probability are avoided.
Paul M. Goldbart and Nigel Goldenfeld
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.003.0019
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
The statistical mechanics of cross-linked macromolecules requires simultaneous treatment of random polymer configurations, excluded-volume interactions, and the quenched disorder of the cross-links, ...
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The statistical mechanics of cross-linked macromolecules requires simultaneous treatment of random polymer configurations, excluded-volume interactions, and the quenched disorder of the cross-links, as well as the topological constraints imposed by impenetrable chains. Such a description was pioneered by Deam and Edwards. This work is reviewed and a discussion presented of subsequent efforts to understand the unique elastic properties of networks as well as the critical phenomena of the vulcanization transition.Less
The statistical mechanics of cross-linked macromolecules requires simultaneous treatment of random polymer configurations, excluded-volume interactions, and the quenched disorder of the cross-links, as well as the topological constraints imposed by impenetrable chains. Such a description was pioneered by Deam and Edwards. This work is reviewed and a discussion presented of subsequent efforts to understand the unique elastic properties of networks as well as the critical phenomena of the vulcanization transition.
Glenn H. Fredrickson
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198567295
- eISBN:
- 9780191717956
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567295.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses elementary statistical mechanical models of ideal chains, i.e., polymers in isolation and not experiencing interactions with other polymers. Freely jointed and bead-spring ...
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This chapter discusses elementary statistical mechanical models of ideal chains, i.e., polymers in isolation and not experiencing interactions with other polymers. Freely jointed and bead-spring discrete chain models are introduced along with continuous Gaussian chain and wormlike chain models. Methods of analysis are based on the solution of Fokker-Planck equations.Less
This chapter discusses elementary statistical mechanical models of ideal chains, i.e., polymers in isolation and not experiencing interactions with other polymers. Freely jointed and bead-spring discrete chain models are introduced along with continuous Gaussian chain and wormlike chain models. Methods of analysis are based on the solution of Fokker-Planck equations.
Michael Munowitz
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195167375
- eISBN:
- 9780199787104
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195167375.003.0010
- Subject:
- Physics, History of Physics
The microscopic laws of motion offer no sense of time, but in the world at large, time marches on. Macroscopic systems progress irreversibly from one state of thermodynamic equilibrium to another, ...
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The microscopic laws of motion offer no sense of time, but in the world at large, time marches on. Macroscopic systems progress irreversibly from one state of thermodynamic equilibrium to another, driven forward by the statistical imperatives of large numbers and overwhelming odds. Energy becomes increasingly dispersed and harder to extract, even as the total amount remains constant. The entropy of the universe grows and grows.Less
The microscopic laws of motion offer no sense of time, but in the world at large, time marches on. Macroscopic systems progress irreversibly from one state of thermodynamic equilibrium to another, driven forward by the statistical imperatives of large numbers and overwhelming odds. Energy becomes increasingly dispersed and harder to extract, even as the total amount remains constant. The entropy of the universe grows and grows.
Robert H. Swendsen
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199646944
- eISBN:
- 9780191775123
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199646944.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book is an introduction to statistical mechanics and thermodynamics. Relevant probability theory is included. Part 1 develops the basic ideas of statistical mechanics, as illustrated by a ...
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This book is an introduction to statistical mechanics and thermodynamics. Relevant probability theory is included. Part 1 develops the basic ideas of statistical mechanics, as illustrated by a complete derivation of the entropy of the classical ideal gas based on Boltzmann's 1877 definition. This leads to a systematic development of thermodynamics in Part 2. Part 3 is devoted to classical statistical mechanics, including a discussion of irreversibility. Part 4 covers quantum statistical mechanics, including lattice vibrations, black-body radiation, Bose-Einstein statistics, Fermi-Dirac statistics, and the Ising model of phase transitions. The text presents many problems that support conceptual development, with a strong emphasis on computational methods. A manual with complete solutions to all problems is available to instructors.Less
This book is an introduction to statistical mechanics and thermodynamics. Relevant probability theory is included. Part 1 develops the basic ideas of statistical mechanics, as illustrated by a complete derivation of the entropy of the classical ideal gas based on Boltzmann's 1877 definition. This leads to a systematic development of thermodynamics in Part 2. Part 3 is devoted to classical statistical mechanics, including a discussion of irreversibility. Part 4 covers quantum statistical mechanics, including lattice vibrations, black-body radiation, Bose-Einstein statistics, Fermi-Dirac statistics, and the Ising model of phase transitions. The text presents many problems that support conceptual development, with a strong emphasis on computational methods. A manual with complete solutions to all problems is available to instructors.
Louis A. Girifalco
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228966
- eISBN:
- 9780191711183
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228966.003.0011
- Subject:
- Physics, History of Physics
Albert Einstein is the only scientist who's genius was comparable to that of Newton's. Their personalities and lifestyles were completely different, but they were both consumed by the desire to know. ...
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Albert Einstein is the only scientist who's genius was comparable to that of Newton's. Their personalities and lifestyles were completely different, but they were both consumed by the desire to know. In 1905, the miracle year, Einstein gave quantum mechanics its true beginning by working out the theory of photoelectricity, created a new statistical mechanics by studying Brownian motion, gave a fully formed theory of special relativity, and derived his famous mass-energy equation. This monumental accomplishment was matched only by Newton's work during the plague years. A decade later, Einstein single handedly developed general relativity, the deepest and most beautiful of all scientific theories.Less
Albert Einstein is the only scientist who's genius was comparable to that of Newton's. Their personalities and lifestyles were completely different, but they were both consumed by the desire to know. In 1905, the miracle year, Einstein gave quantum mechanics its true beginning by working out the theory of photoelectricity, created a new statistical mechanics by studying Brownian motion, gave a fully formed theory of special relativity, and derived his famous mass-energy equation. This monumental accomplishment was matched only by Newton's work during the plague years. A decade later, Einstein single handedly developed general relativity, the deepest and most beautiful of all scientific theories.
