Statistical Mechanics and Entropy

"Statistical Mechanics and Entropy" is an edited book consisting of 16 contemporaneous open-access articles that highlight different aspects of the definition of entropy in statistical mechanics and other fields. The book includes a reflection on the real physical meaning of thermodynamic entropy, and several misconceptions regarding the violation of the second law of thermodynamics by perpetual motion machines, Maxwell's demon, vortex tube, etc. It overviews the concept of generalized Boltzmann-Gibbs entropy in dynamical systems (e.g. Kolmogorov-Sinai entropy), information theory (e.g. Renyi and Shannon entropies), and statistical physics (e.g. Tsallis entropy). It includes quantum modifications and extensions of equilibrium statistical mechanics. Fundamental laws of nature and thermodynamics are expanded from classical simple systems to quantum systems, as well as to more complex systems in biology, cosmology, economy and communication networks. Reading this book requires some knowledge in thermodynamics, calculus and differential equations. This book is intended to reach an academic audience ranging from undergraduate students to experienced researchers. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Chapter 1 The Elusive Nature of Entropy and its Physical Meaning Abstract Introduction From Carnot’s Ingenious Reasoning of Reversible Cycles to Clausius’ Definition of Entropy Clausius Equality (Entropy) and Linequality (Entropy Generation) Physical Meaning of Entropy: Thermal Displacement of Thermal Energy (Dynamic Thermal-Volume) Physical Meaning of Entropy: A Measure of Thermal Disorder Conclusions: Physical Meaning of Entropy References Chapter 2 The Second Law and Entropy Misconceptions Demystified Abstract Introduction The Essence of “Mass-Energy, Entropy and the Second Law Fundamentals” The Three Essential “Entropy and Second Law Misconceptions” Other Typical “Entropy and Second Law Misconceptions” Further Comments References and Note Chapter 3 Thermodynamics, Statistical Mechanics and Entropy Abstract Introduction Thermodynamic Postulates The Laws of Thermodynamics Macroscopic Probabilities for Classical Systems The Boltzmann Entropy, Sb, for Classical Systems The Gibbs Entropy, Sg, for Classical Systems The Canonical Entropy, Sc, for Classical Systems The Grand Canonical Entropy, Sgc, for Classical Systems Quantum Statistical Mechanics First-Order Phase Transitions Collections of Non-Interacting Objects Negative Temperatures Discussion References and Notes Chapter 4 Entropy and its Correlations with Other Related Quantities Abstract Introduction Exergy And Entropy Unavailable Potential Energy Per Unit Environmental Temperature Conclusions Acknowledgments References Chapter 5 A Brief Review of Generalized Entropies Abstract Introduction Generalized Entropies Hanel–Thurner Exponents Asymptotic Relation Between the HT Exponent C and the Diffusion Scaling Exponent Conclusions Author Contributions Funding Acknowledgments Appendix A Appendix B Appendix C References Chapter 6 Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere Abstract Introduction Non-Boltzmannian Entropy Measures and Distributions Further Connections Conclusions and Perspectives Funding Acknowledgments References and Notes Chapter 7 The Gibbs Paradox: Lessons from Thermodynamics Abstract Introduction Formulating the Gibbs Paradox in Thermodynamics Formulating the Gibbs Paradox in Statistical Mechanics References Chapter 8 The Gibbs Paradox and Particle Individuality Abstract Introduction The Gibbs Paradox in Thermodynamics The Gibbs Paradox in Statistical Mechanics Proposed Solutions of the Statistical Paradox Quantum Mechanics Conclusions References Chapter 9 Mixing Indistinguishable Systems Leads to a Quantum Gibbs Paradox Abstract Introduction Results Discussion Methods Acknowledgements Contributions Supplementary Information References Chapter 10 Thermal Quantum Spacetime Abstract Introduction Background Independent Equilibrium Statistical Mechanics Equilibrium Statistical Mechanics in Quantum Gravity Conclusions and Outlook Acknowledgments References Chapter 11 Thermodynamics, Stability and Hawking–Page Transition of Black Holes from Non-Extensive Statistical Mechanics in Quantum Geometry Abstract Introduction Quantum Theory in LQG Nonextensive Entropy Bekenstein-Hawking and Tsallis Entropy for Black Hole Thermodynamic Stability of Black Holes Conclusion References Chapter 12 Gravitational Entropy and Inflation Abstract Introduction A Flat Universe Model With Ideal Gas and Live Measures of Gravitational Entropy Gravitational Entropy in the Plane-Symmetric Bianchi Type I Universe Gravitational Entropy in LTB Models With Live A Model of Entropy Generation At the End of The Inflationary Era The Concept of a Maximal Entropy For the Universe Entropy Gap and the Arrow of Time Conclusions References Chapter 13 Statistical Mechanics and Thermodynamics of Viral Evolution Abstract Introduction Methods This is the Entry Target for Regularcells Way of Entering It Results and Discussion Conclusions Acknowledgments References Chapter 14 Energy, Entropy and Exergy in Communication Networks Abstract Introduction Analogies Between Communication and Thermodynamic Systems Exergy in Communication Networks Conclusions Acknowledgments References Chapter 15 Statistical Mechanics of Zooplankton Abstract Introduction Statistical Mechanics and Thermodynamics Materials and Methods Results Outlook Acknowledgments References Chapter 16 Statistical Thermodynamics of Economic Systems Abstract Introduction Statistical Thermodynamics Hypothetical Economic Systems Phase Transitions Discussion and Conclusions Acknowledgments References Index Back Cover "Statistical Mechanics and Entropy" is an edited book consisting of 16 contemporaneous open-access articles that highlight different aspects of the definition of entropy in statistical mechanics and other fields. The book includes a reflection on the real physical meaning of thermodynamic entropy, and several misconceptions regarding the violation of the second law of thermodynamics by perpetual motion machines, Maxwell's demon, vortex tube, etc. It overviews the concept of generalized Boltzmann-Gibbs entropy in dynamical systems (e.g. Kolmogorov-Sinai entropy), information theory (e.g. Rényi and Shannon entropies), and statistical physics (e.g. Tsallis entropy). It includes quantum modifications and extensions of equilibrium statistical mechanics. Fundamental laws of nature and thermodynamics are expanded from classical simple systems to quantum systems, as well as to more complex systems in biology, cosmology, economy and communication networks. Reading this book requires some knowledge in thermodynamics, calculus and differential equations. This book is intended to reach an academic audience ranging from undergraduate students to experienced researchers.