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Journal of chemical theory and computation : JCTC
| Journal of chemical theory and computation : JCTC |
| Pubbl/distr/stampa | Washington, D.C., : American Chemical Society, 2005- |
| Disciplina | 541.2 |
| Soggetto topico |
Quantum chemistry
Molecular dynamics Statistical mechanics Molecular Biology Biomechanical Phenomena Chemistry Biochemistry Chimie quantique Mécanique statistique Chimie Biochimie Biomécanique |
| Soggetto genere / forma |
Periodical
Periodicals. Ressource Internet (Descripteur de forme) Périodique électronique (Descripteur de forme) |
| ISSN | 1549-9626 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti |
JCTC
Chemical theory and computation |
| Record Nr. | UNINA-9910143532003321 |
| Washington, D.C., : American Chemical Society, 2005- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Journal of statistical mechanics : theory and experiment
| Journal of statistical mechanics : theory and experiment |
| Pubbl/distr/stampa | Bristol, England, : Institute of Physics Pub. |
| Soggetto topico |
Statistical mechanics
Mechanics - Statistical methods Mekanik |
| Soggetto genere / forma | Periodicals. |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti |
J. stat. mech
JSTAT |
| Record Nr. | UNISA-996215409803316 |
| Bristol, England, : Institute of Physics Pub. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Journal of statistical mechanics : theory and experiment
| Journal of statistical mechanics : theory and experiment |
| Pubbl/distr/stampa | Bristol, England, : Institute of Physics Pub. |
| Soggetto topico |
Statistical mechanics
Mechanics - Statistical methods Mekanik |
| Soggetto genere / forma | Periodicals. |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti |
J. stat. mech
JSTAT |
| Record Nr. | UNINA-9910142877203321 |
| Bristol, England, : Institute of Physics Pub. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Korepin festschrift : from statistical mechanics to quantum information science : a collection of articles written in honor of the 60th birthday of Vladimir Korepin / / editors, Leong Chuan Kwek, National University of Singapore & Nanyang Technological University, Singapore, Simone Severini, University College London, UK, Haibin Su, Nanyang Technological University, Singapore
| The Korepin festschrift : from statistical mechanics to quantum information science : a collection of articles written in honor of the 60th birthday of Vladimir Korepin / / editors, Leong Chuan Kwek, National University of Singapore & Nanyang Technological University, Singapore, Simone Severini, University College London, UK, Haibin Su, Nanyang Technological University, Singapore |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (xx, 217 pages) : illustrations (some color) |
| Disciplina | 003.54 |
| Collana | Gale eBooks |
| Soggetto topico |
Information science
Quantum computers Quantum theory Statistical mechanics |
| ISBN | 981-4460-32-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; CONTENTS; Organizing Committee; List of Speakers; Photos; Chapter 1: Cancellation of Ultra-Violet Infinities in One Loop Gravity V. E. Korepin; 1. Introduction; 2. Covariant Quantization; 3. Cancellation of Infinities in one Loop Approximation; 4. Finite Part of the Generating Functional of the Scattering Matrix; 5. One Loop Diagram with Two Vertices; References; Chapter 2: Quantum Discord in a Spin System with Symmetry Breaking B. Tomasello, D. Rossini, A. Hamma and L. Amico; 1. Introduction; 2. Quantum, Classical, and Total Correlations; 3. The XY Model in Transverse Field
3.1. The Phase Diagram 4. Classical and Quantum Correlations in the Model; 5. Analysis of Quantum Discord at T = 0; 6. Quantum Discord at Finite Temperature; 7. Discussions; Acknowledgments; References; Chapter 3: Entanglement from the Dynamics of an Ideal Bose Gas in a Lattice S. Bose; 1. Introduction; Acknowledgment; References; Chapter 4: Aspects of the Riemannian Geometry of Quantum Computation H. E. Brandt; 1. Introduction; 2. Riemannian Geometry of SU(2n); 3. Summary; Acknowledgment; References; Chapter 5: Quantum Mechanics and the Role of Time: Are Quantum Systems Markovian? T. Durt 1. Introduction 2. Do Quantum Dice Remember? - Experimental Tests; 2.1. Bohm-Bub's model and the Papaliolos experiment; 2.2. Buonomano's model and the Summhammer experiment; 2.3. Hidden measurement approach and the Paris-Nord experiment; 2.3.1. The Poissonian paradigm; 2.3.2. Departures from the Poissonian paradigm; 2.3.3. Recent results; 2.4. Shnoll's hypotheses and the Brussels experiment; 3. Sheldrake and Smolin's Models, and a Related Experimental Proposal; 3.1. Sheldrake's model; 3.2. Smolin's model; 3.3. Unfalsifiability of Sheldrake and Smolin's models - New experimental proposals 4. Conclusions Acknowledgments; References; Chapter 6: Explicit Formula of the Separability Criterion for Continuous Variables Systems K. Fujikawa; 1. Introduction and Summary; 2. Details of Analyses; 2.1. Simon's criterion; 2.2. Gaussian states and P-representation; 2.3. Duan-Giedke-Chirac-Zoller criterion; 2.4. Hierarchy of separability criterions; 3. Discussion and Related References; References; Chapter 7: Yang-Baxter Equations in Quantum Information M.-L. Ge and K. Xue; 1. Introduction; 2. Two Types of Braiding Matrices. Yang-Baxter Equation and Temperley-Lieb Algebra Chapter 8: Nondistillable Entanglement Guarantees Distillable Entanglement L. Chen and M. Hayashi |
| Record Nr. | UNINA-9910779882703321 |
| Hackensack, NJ, : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Korepin festschrift : from statistical mechanics to quantum information science : a collection of articles written in honor of the 60th birthday of Vladimir Korepin / / editors, Leong Chuan Kwek, National University of Singapore & Nanyang Technological University, Singapore, Simone Severini, University College London, UK, Haibin Su, Nanyang Technological University, Singapore
| The Korepin festschrift : from statistical mechanics to quantum information science : a collection of articles written in honor of the 60th birthday of Vladimir Korepin / / editors, Leong Chuan Kwek, National University of Singapore & Nanyang Technological University, Singapore, Simone Severini, University College London, UK, Haibin Su, Nanyang Technological University, Singapore |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (xx, 217 pages) : illustrations (some color) |
| Disciplina | 003.54 |
| Collana | Gale eBooks |
| Soggetto topico |
Information science
Quantum computers Quantum theory Statistical mechanics |
| ISBN | 981-4460-32-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; CONTENTS; Organizing Committee; List of Speakers; Photos; Chapter 1: Cancellation of Ultra-Violet Infinities in One Loop Gravity V. E. Korepin; 1. Introduction; 2. Covariant Quantization; 3. Cancellation of Infinities in one Loop Approximation; 4. Finite Part of the Generating Functional of the Scattering Matrix; 5. One Loop Diagram with Two Vertices; References; Chapter 2: Quantum Discord in a Spin System with Symmetry Breaking B. Tomasello, D. Rossini, A. Hamma and L. Amico; 1. Introduction; 2. Quantum, Classical, and Total Correlations; 3. The XY Model in Transverse Field
3.1. The Phase Diagram 4. Classical and Quantum Correlations in the Model; 5. Analysis of Quantum Discord at T = 0; 6. Quantum Discord at Finite Temperature; 7. Discussions; Acknowledgments; References; Chapter 3: Entanglement from the Dynamics of an Ideal Bose Gas in a Lattice S. Bose; 1. Introduction; Acknowledgment; References; Chapter 4: Aspects of the Riemannian Geometry of Quantum Computation H. E. Brandt; 1. Introduction; 2. Riemannian Geometry of SU(2n); 3. Summary; Acknowledgment; References; Chapter 5: Quantum Mechanics and the Role of Time: Are Quantum Systems Markovian? T. Durt 1. Introduction 2. Do Quantum Dice Remember? - Experimental Tests; 2.1. Bohm-Bub's model and the Papaliolos experiment; 2.2. Buonomano's model and the Summhammer experiment; 2.3. Hidden measurement approach and the Paris-Nord experiment; 2.3.1. The Poissonian paradigm; 2.3.2. Departures from the Poissonian paradigm; 2.3.3. Recent results; 2.4. Shnoll's hypotheses and the Brussels experiment; 3. Sheldrake and Smolin's Models, and a Related Experimental Proposal; 3.1. Sheldrake's model; 3.2. Smolin's model; 3.3. Unfalsifiability of Sheldrake and Smolin's models - New experimental proposals 4. Conclusions Acknowledgments; References; Chapter 6: Explicit Formula of the Separability Criterion for Continuous Variables Systems K. Fujikawa; 1. Introduction and Summary; 2. Details of Analyses; 2.1. Simon's criterion; 2.2. Gaussian states and P-representation; 2.3. Duan-Giedke-Chirac-Zoller criterion; 2.4. Hierarchy of separability criterions; 3. Discussion and Related References; References; Chapter 7: Yang-Baxter Equations in Quantum Information M.-L. Ge and K. Xue; 1. Introduction; 2. Two Types of Braiding Matrices. Yang-Baxter Equation and Temperley-Lieb Algebra Chapter 8: Nondistillable Entanglement Guarantees Distillable Entanglement L. Chen and M. Hayashi |
| Record Nr. | UNINA-9910824775403321 |
| Hackensack, NJ, : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures in statistical mechanics / G.E. Uhlenbeck and G.W. Ford ; with an appendix by E.W. Montroll
| Lectures in statistical mechanics / G.E. Uhlenbeck and G.W. Ford ; with an appendix by E.W. Montroll |
| Autore | Uhlenbeck, G.E. |
| Pubbl/distr/stampa | Providence, RI : American Mathematical Society, 1963 |
| Descrizione fisica | x, 181 p. : ill. ; 24 cm. |
| Altri autori (Persone) |
Ford, G.W.
Montroll, E.W. |
| Collana | Lectures in applied mathematics ; 1 |
| Soggetto topico | Statistical mechanics |
| Classificazione |
53.1.62
53.1.64 QC174.82.U354 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001049809707536 |
Uhlenbeck, G.E.
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| Providence, RI : American Mathematical Society, 1963 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Lectures on selected topics in statistical mechanics / D. Ter Haar
| Lectures on selected topics in statistical mechanics / D. Ter Haar |
| Autore | Haar, D. Ter |
| Pubbl/distr/stampa | Oxford : Pergamon Press, 1977 |
| Descrizione fisica | vii, 124 p. : ill. ; 26 cm. |
| Disciplina | 530.13 |
| Collana | International series in natural philosophy ; 92 |
| Soggetto topico | Statistical mechanics |
| ISBN | 0080179371 |
| Classificazione |
AMS 82-01
AMS 82-XX QC174.82 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001069369707536 |
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Haar, D. Ter
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| Oxford : Pergamon Press, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Lectures on statistical mechanics / by M. G. Bowler
| Lectures on statistical mechanics / by M. G. Bowler |
| Autore | Bowler, M. G. |
| Edizione | [1st ed] |
| Pubbl/distr/stampa | Oxford : Pergamon Press, 1982 |
| Descrizione fisica | ix, 120 p. ; 24 cm. |
| Disciplina | 530.13 |
| Soggetto topico | Statistical mechanics |
| ISBN | 0080265154 |
| Classificazione |
AMS 82-01
QC174.8.B68 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001069539707536 |
|
Bowler, M. G.
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| Oxford : Pergamon Press, 1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Making sense of statistical mechanics / / J. Bricmont
| Making sense of statistical mechanics / / J. Bricmont |
| Autore | Bricmont J (Jean) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (375 pages) |
| Disciplina | 530.13 |
| Collana | Undergraduate lecture notes in physics |
| Soggetto topico | Statistical mechanics |
| ISBN |
9783030917944
9783030917937 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Contents -- 1 Introduction -- 2 Probability -- 2.1 Introduction -- 2.2 ``Subjective'' Versus ``Objective'' Probabilities -- 2.2.1 The Indifference Principle -- 2.2.2 Cox' ``Axioms'' and Theorem -- 2.2.3 Bayesian Updating -- 2.2.4 Objections to the ``Subjective'' Approach -- 2.2.5 Bertrand's Paradox -- 2.3 The Law of Large Numbers -- 2.3.1 A Simple Example -- 2.3.2 A More General Result -- 2.3.3 Corrections to the Law of Large Numbers -- 2.4 The Law of Large Numbers and the Frequentist Interpretation -- 2.5 Explanations and Probabilistic Explanations -- 2.6 Final Remarks -- 2.7 Summary -- 2.8 Exercises -- 2.A Appendix A: Measure Theory -- 2.A.1 Definition of a Measure -- 2.A.2 Constructions of Measures -- 2.A.3 Integration -- 2.A.4 Approximation of Integrals -- 2.A.5 Invariant Measures -- 2.A.6 Probability Densities, Marginal and Conditional Probabilities -- 2.A.7 Cantor Sets and Measures -- 2.B Appendix B: Proofs of the Law of Large Numbers and of the Central Limit Theorem -- 3 Classical Mechanics -- 3.1 Introduction -- 3.2 Newton's Laws -- 3.3 Hamilton's Equations -- 3.3.1 The Hamiltonian Flow -- 3.3.2 Conservation of Energy -- 3.4 Liouville's Theorem and Measure -- 3.4.1 Liouville's Theorem -- 3.4.2 The Liouville Measure -- 3.5 Time Reversibility -- 3.6 Summary -- 3.7 Exercises -- 4 Dynamical Systems -- 4.1 Introduction -- 4.2 Poincaré's Recurrence Theorem, or The Eternal Return -- 4.2.1 Proof of Poincaré's Recurrence Theorem -- 4.3 Ergodic Theorems -- 4.3.1 Examples and Applications -- 4.3.2 Ergodicity and the Law of Large Numbers -- 4.4 Mixing -- 4.5 Sensitive Dependence on Initial Conditions -- 4.6 Statistical Theory of Dynamical Systems -- 4.6.1 Itineraries and Coding -- 4.6.2 Strange Attractors -- 4.7 Dynamical Entropies -- 4.8 Determinism and Predictability -- 4.9 Summary -- 4.10 Exercises -- 5 Thermodynamics -- 5.1 Introduction.
5.2 The Zeroth Law -- 5.3 The First Law -- 5.3.1 Work -- 5.3.2 Heat -- 5.4 The Second Law -- 5.4.1 The Carnot Cycle -- 5.4.2 Proof of the Equivalence Between Lord Kelvin's Version and Clausius' Version of the Second Law -- 5.5 The Thermodynamic Entropy -- 5.5.1 Definition of the Entropy Function -- 5.5.2 The Second Law or the Increase of the Thermodynamic Entropy -- 5.6 Other Thermodynamic Functions -- 5.6.1 The Particle Number -- 5.6.2 Fundamental Relations -- 5.6.3 The Helmholtz Free Energy -- 5.6.4 The Grand Potential -- 5.6.5 The Principle of Maximum Entropy and Equilibrium Conditions -- 5.7 An Example: The Ideal Gas -- 5.7.1 Mathematical Identities and the Gibbs-Duhem Relations -- 5.7.2 Derivation of the Fundamental Relation for an Ideal Gas -- 5.7.3 The Fundamental Relation in Other Variables for an Ideal Gas -- 5.7.4 Adiabatic Transformations -- 5.7.5 Be Careful with Derivatives! -- 5.8 What Is All This Good For? -- 5.9 Summary -- 5.10 Exercises -- 5.A Differential Forms -- 5.B Legendre Transforms -- 5.B.1 Mathematical Definition -- 5.B.2 Physical Applications -- 5.C Physical Units and Boltzmann's Constant -- 6 Equilibrium Statistical Mechanics -- 6.1 Microstates and Macrostates -- 6.2 Dominance of the Equilibrium Macrostate -- 6.3 Typicality -- 6.4 Entropy in Equilibrium -- 6.5 Other Equilibrium Potentials -- 6.6 The Equilibrium Ensembles -- 6.6.1 Definition of the Ensembles -- 6.6.2 The Gibbs Entropy -- 6.6.3 Equivalence of Ensembles -- 6.6.4 The Meaning of Ensembles -- 6.7 Justification of the Entropy Formula (6.4.2) -- 6.8 What Justifies the Microcanonical Distribution? -- 6.9 Summary -- 6.10 Exercises -- 6.A Asymptotics -- 6.A.1 Laplace's Method -- 6.A.2 Stirling's Formula -- 6.B ``Derivation'' of Formula (6.5.4) -- 6.C An Intuitive Formula for the Entropy -- 7 Information-Theoretic and Predictive Statistical Mechanics -- 7.1 Introduction. 7.2 The Shannon Entropy -- 7.3 The Maximum Entropy Principle -- 7.4 The Ensembles -- 7.5 Continuous Distributions and Relative Entropy -- 7.6 ``Derivation'' of the Second Law -- 7.7 Shannon's Entropy and Communication -- 7.7.1 Information Content of a Message -- 7.7.2 Encoding Messages -- 7.8 Evaluation of the Information Theoretic Approach -- 7.8.1 What Do Probabilities Mean Here? -- 7.8.2 Jaynes' Approach -- 7.9 Summary -- 7.10 Exercises -- 7.A Proof that (7.2.6) Implies A(N)= klogN -- 7.B Jensen's Inequality -- 8 Approach to Equilibrium -- 8.1 Boltzmann's Scheme -- 8.1.1 Microstates and Macrostates -- 8.1.2 Derivation of Macroscopic Laws from Microscopic Ones -- 8.1.3 Solution of the (Apparent) Reversibility Paradox -- 8.1.4 Irreversibility and Probabilistic Explanations -- 8.1.5 Time Dependent Boltzmann Entropy and the Second Law -- 8.2 Answers to the Classical Objections -- 8.2.1 Objections from Loschmidt and Zermelo -- 8.2.2 An Objection from Poincaré -- 8.2.3 Objections to Typicality Arguments -- 8.3 Ergodicity, Mixing, and Other Wrong Turns -- 8.3.1 Ergodicity -- 8.3.2 Mixing -- 8.3.3 The Brussels-Austin School -- 8.3.4 Real Systems Are Never Isolated -- 8.4 Maxwell's Demon -- 8.5 The Origins of the Low Entropy States -- 8.6 The Boltzmann Equation -- 8.6.1 The Relation Between the Boltzmann Equation and the Full Evolution of Measures -- 8.7 Simple Models -- 8.7.1 Ehrenfest's Urns -- 8.7.2 Kac Ring Model -- 8.7.3 Uncoupled Baker's Maps -- 8.7.4 Ideal Gas in a Box -- 8.7.5 The Abiabatic Piston -- 8.8 Boltzmann Versus Gibbs Entropies -- 8.8.1 Another Time Evolution of Measures -- 8.8.2 The Example of the Uncoupled Baker's Maps of Sect.8.7.3 -- 8.9 Conclusion: Are Entropy and Irreversibility Subjective? -- 8.10 Dynamical Systems Vs Statistical Mechanics -- 8.11 Summary -- 8.12 Exercises -- 8.A Boltzmannian Quotes. 8.B Quotes Critical of Boltzmann -- 9 Phase Transitions -- 9.1 Phenomenology -- 9.2 Lattice Models and Gibbs States -- 9.3 Mean Field Theory -- 9.4 One Dimension -- 9.5 High Temperature Expansions -- 9.6 Low Temperatures and the Peierls Argument -- 9.7 Other Models -- 9.7.1 Trivial Extensions -- 9.7.2 Long Range Interactions -- 9.7.3 Many Body Interactions -- 9.7.4 Continuous Spins -- 9.7.5 Models with a Continuous Symmetry -- 9.7.6 Non Translation Invariant Gibbs States -- 9.8 The Pirogov-Sinai Theory -- 9.8.1 A Simple Example -- 9.8.2 The General Pirogov-Sinai Theory -- 9.9 Critical Points -- 9.9.1 Phenomenology -- 9.9.2 Mean Field Theory -- 9.9.3 More Realistic Models -- 9.10 Summary -- 9.11 Exercises -- 10 Conclusion: Statistical Mechanics and Reductionism -- 11 Hints and Solutions for the Exercises -- 11.1 Exercises of Chap.2摥映數爠eflinkchap222 -- 11.2 Exercises of Chap.3摥映數爠eflinkchap333 -- 11.3 Exercises of Chap.4摥映數爠eflinkchap444 -- 11.4 Exercises of Chap.5摥映數爠eflinkchap555 -- 11.5 Exercises of Chap.6摥映數爠eflinkchap666 -- 11.6 Exercises of Chap.7摥映數爠eflinkchap777 -- 11.7 Exercises of Chap.8摥映數爠eflinkchap888 -- 11.8 Exercises of Chap.9摥映數爠eflinkchap999 -- Appendix Glossary -- Appendix Suggested Reading -- Appendix References -- -- Index. |
| Record Nr. | UNINA-9910544865103321 |
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Bricmont J (Jean)
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Making sense of statistical mechanics / / J. Bricmont
| Making sense of statistical mechanics / / J. Bricmont |
| Autore | Bricmont J (Jean) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (375 pages) |
| Disciplina | 530.13 |
| Collana | Undergraduate lecture notes in physics |
| Soggetto topico | Statistical mechanics |
| ISBN |
9783030917944
9783030917937 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Contents -- 1 Introduction -- 2 Probability -- 2.1 Introduction -- 2.2 ``Subjective'' Versus ``Objective'' Probabilities -- 2.2.1 The Indifference Principle -- 2.2.2 Cox' ``Axioms'' and Theorem -- 2.2.3 Bayesian Updating -- 2.2.4 Objections to the ``Subjective'' Approach -- 2.2.5 Bertrand's Paradox -- 2.3 The Law of Large Numbers -- 2.3.1 A Simple Example -- 2.3.2 A More General Result -- 2.3.3 Corrections to the Law of Large Numbers -- 2.4 The Law of Large Numbers and the Frequentist Interpretation -- 2.5 Explanations and Probabilistic Explanations -- 2.6 Final Remarks -- 2.7 Summary -- 2.8 Exercises -- 2.A Appendix A: Measure Theory -- 2.A.1 Definition of a Measure -- 2.A.2 Constructions of Measures -- 2.A.3 Integration -- 2.A.4 Approximation of Integrals -- 2.A.5 Invariant Measures -- 2.A.6 Probability Densities, Marginal and Conditional Probabilities -- 2.A.7 Cantor Sets and Measures -- 2.B Appendix B: Proofs of the Law of Large Numbers and of the Central Limit Theorem -- 3 Classical Mechanics -- 3.1 Introduction -- 3.2 Newton's Laws -- 3.3 Hamilton's Equations -- 3.3.1 The Hamiltonian Flow -- 3.3.2 Conservation of Energy -- 3.4 Liouville's Theorem and Measure -- 3.4.1 Liouville's Theorem -- 3.4.2 The Liouville Measure -- 3.5 Time Reversibility -- 3.6 Summary -- 3.7 Exercises -- 4 Dynamical Systems -- 4.1 Introduction -- 4.2 Poincaré's Recurrence Theorem, or The Eternal Return -- 4.2.1 Proof of Poincaré's Recurrence Theorem -- 4.3 Ergodic Theorems -- 4.3.1 Examples and Applications -- 4.3.2 Ergodicity and the Law of Large Numbers -- 4.4 Mixing -- 4.5 Sensitive Dependence on Initial Conditions -- 4.6 Statistical Theory of Dynamical Systems -- 4.6.1 Itineraries and Coding -- 4.6.2 Strange Attractors -- 4.7 Dynamical Entropies -- 4.8 Determinism and Predictability -- 4.9 Summary -- 4.10 Exercises -- 5 Thermodynamics -- 5.1 Introduction.
5.2 The Zeroth Law -- 5.3 The First Law -- 5.3.1 Work -- 5.3.2 Heat -- 5.4 The Second Law -- 5.4.1 The Carnot Cycle -- 5.4.2 Proof of the Equivalence Between Lord Kelvin's Version and Clausius' Version of the Second Law -- 5.5 The Thermodynamic Entropy -- 5.5.1 Definition of the Entropy Function -- 5.5.2 The Second Law or the Increase of the Thermodynamic Entropy -- 5.6 Other Thermodynamic Functions -- 5.6.1 The Particle Number -- 5.6.2 Fundamental Relations -- 5.6.3 The Helmholtz Free Energy -- 5.6.4 The Grand Potential -- 5.6.5 The Principle of Maximum Entropy and Equilibrium Conditions -- 5.7 An Example: The Ideal Gas -- 5.7.1 Mathematical Identities and the Gibbs-Duhem Relations -- 5.7.2 Derivation of the Fundamental Relation for an Ideal Gas -- 5.7.3 The Fundamental Relation in Other Variables for an Ideal Gas -- 5.7.4 Adiabatic Transformations -- 5.7.5 Be Careful with Derivatives! -- 5.8 What Is All This Good For? -- 5.9 Summary -- 5.10 Exercises -- 5.A Differential Forms -- 5.B Legendre Transforms -- 5.B.1 Mathematical Definition -- 5.B.2 Physical Applications -- 5.C Physical Units and Boltzmann's Constant -- 6 Equilibrium Statistical Mechanics -- 6.1 Microstates and Macrostates -- 6.2 Dominance of the Equilibrium Macrostate -- 6.3 Typicality -- 6.4 Entropy in Equilibrium -- 6.5 Other Equilibrium Potentials -- 6.6 The Equilibrium Ensembles -- 6.6.1 Definition of the Ensembles -- 6.6.2 The Gibbs Entropy -- 6.6.3 Equivalence of Ensembles -- 6.6.4 The Meaning of Ensembles -- 6.7 Justification of the Entropy Formula (6.4.2) -- 6.8 What Justifies the Microcanonical Distribution? -- 6.9 Summary -- 6.10 Exercises -- 6.A Asymptotics -- 6.A.1 Laplace's Method -- 6.A.2 Stirling's Formula -- 6.B ``Derivation'' of Formula (6.5.4) -- 6.C An Intuitive Formula for the Entropy -- 7 Information-Theoretic and Predictive Statistical Mechanics -- 7.1 Introduction. 7.2 The Shannon Entropy -- 7.3 The Maximum Entropy Principle -- 7.4 The Ensembles -- 7.5 Continuous Distributions and Relative Entropy -- 7.6 ``Derivation'' of the Second Law -- 7.7 Shannon's Entropy and Communication -- 7.7.1 Information Content of a Message -- 7.7.2 Encoding Messages -- 7.8 Evaluation of the Information Theoretic Approach -- 7.8.1 What Do Probabilities Mean Here? -- 7.8.2 Jaynes' Approach -- 7.9 Summary -- 7.10 Exercises -- 7.A Proof that (7.2.6) Implies A(N)= klogN -- 7.B Jensen's Inequality -- 8 Approach to Equilibrium -- 8.1 Boltzmann's Scheme -- 8.1.1 Microstates and Macrostates -- 8.1.2 Derivation of Macroscopic Laws from Microscopic Ones -- 8.1.3 Solution of the (Apparent) Reversibility Paradox -- 8.1.4 Irreversibility and Probabilistic Explanations -- 8.1.5 Time Dependent Boltzmann Entropy and the Second Law -- 8.2 Answers to the Classical Objections -- 8.2.1 Objections from Loschmidt and Zermelo -- 8.2.2 An Objection from Poincaré -- 8.2.3 Objections to Typicality Arguments -- 8.3 Ergodicity, Mixing, and Other Wrong Turns -- 8.3.1 Ergodicity -- 8.3.2 Mixing -- 8.3.3 The Brussels-Austin School -- 8.3.4 Real Systems Are Never Isolated -- 8.4 Maxwell's Demon -- 8.5 The Origins of the Low Entropy States -- 8.6 The Boltzmann Equation -- 8.6.1 The Relation Between the Boltzmann Equation and the Full Evolution of Measures -- 8.7 Simple Models -- 8.7.1 Ehrenfest's Urns -- 8.7.2 Kac Ring Model -- 8.7.3 Uncoupled Baker's Maps -- 8.7.4 Ideal Gas in a Box -- 8.7.5 The Abiabatic Piston -- 8.8 Boltzmann Versus Gibbs Entropies -- 8.8.1 Another Time Evolution of Measures -- 8.8.2 The Example of the Uncoupled Baker's Maps of Sect.8.7.3 -- 8.9 Conclusion: Are Entropy and Irreversibility Subjective? -- 8.10 Dynamical Systems Vs Statistical Mechanics -- 8.11 Summary -- 8.12 Exercises -- 8.A Boltzmannian Quotes. 8.B Quotes Critical of Boltzmann -- 9 Phase Transitions -- 9.1 Phenomenology -- 9.2 Lattice Models and Gibbs States -- 9.3 Mean Field Theory -- 9.4 One Dimension -- 9.5 High Temperature Expansions -- 9.6 Low Temperatures and the Peierls Argument -- 9.7 Other Models -- 9.7.1 Trivial Extensions -- 9.7.2 Long Range Interactions -- 9.7.3 Many Body Interactions -- 9.7.4 Continuous Spins -- 9.7.5 Models with a Continuous Symmetry -- 9.7.6 Non Translation Invariant Gibbs States -- 9.8 The Pirogov-Sinai Theory -- 9.8.1 A Simple Example -- 9.8.2 The General Pirogov-Sinai Theory -- 9.9 Critical Points -- 9.9.1 Phenomenology -- 9.9.2 Mean Field Theory -- 9.9.3 More Realistic Models -- 9.10 Summary -- 9.11 Exercises -- 10 Conclusion: Statistical Mechanics and Reductionism -- 11 Hints and Solutions for the Exercises -- 11.1 Exercises of Chap.2摥映數爠eflinkchap222 -- 11.2 Exercises of Chap.3摥映數爠eflinkchap333 -- 11.3 Exercises of Chap.4摥映數爠eflinkchap444 -- 11.4 Exercises of Chap.5摥映數爠eflinkchap555 -- 11.5 Exercises of Chap.6摥映數爠eflinkchap666 -- 11.6 Exercises of Chap.7摥映數爠eflinkchap777 -- 11.7 Exercises of Chap.8摥映數爠eflinkchap888 -- 11.8 Exercises of Chap.9摥映數爠eflinkchap999 -- Appendix Glossary -- Appendix Suggested Reading -- Appendix References -- -- Index. |
| Record Nr. | UNISA-996466841803316 |
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Bricmont J (Jean)
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Statistical mechanics
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