"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.
Author(s): Olga Moreira
Publisher: Arcler Press
Year: 2022
Language: English
Pages: xxiii; 456
City: Burlington
Tags: Thermodynamics; Entropy; Information theory; Statistical physics
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
