A Farewell to Entropy Statistical Thermodynamics Based on Information 1st Edition by Arieh Ben Naim ISBN 978-9812707079 9812707077
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Product details:
ISBN 10: 9812707077
ISBN 13: 978-9812707079
Author: Arieh Ben-Naim
The principal message of this book is that thermodynamics and statistical mechanics will benefit from replacing the unfortunate, misleading and mysterious term “entropy” with a more familiar, meaningful and appropriate term such as information, missing information or uncertainty. This replacement would facilitate the interpretation of the “driving force” of many processes in terms of informational changes and dispel the mystery that has always enshrouded entropy.It has been 140 years since Clausius coined the term “entropy”; almost 50 years since Shannon developed the mathematical theory of “information” — subsequently renamed “entropy”. In this book, the author advocates replacing “entropy” by “information”, a term that has become widely used in many branches of science.The author also takes a new and bold approach to thermodynamics and statistical mechanics. Information is used not only as a tool for predicting distributions but as the fundamental cornerstone concept of thermodynamics, held until now by the term “entropy”.The topics covered include the fundamentals of probability and information theory; the general concept of information as well as the particular concept of information as applied in thermodynamics; the re-derivation of the Sackur-Tetrode equation for the entropy of an ideal gas from purely informational arguments; the fundamental formalism of statistical mechanics; and many examples of simple processes the “driving force” for which is analyzed in terms of information.
Table of contents:
1 Introduction
1.1 A Brief History of Temperature and Entropy
1.2 The Association of Entropy with Disorder
1.3 The Association of Entropy with Missing Information
2 Elements of Probability Theory
2.1 Introduction
2.2 The Axiomatic Approach
2.2.1 The sample space, denoted Ω
2.2.2 The field of events, denoted F
2.2.3 The probability function, denoted P
2.3 The Classical Definition
2.4 The Relative Frequency Definition
2.5 Independent Events and Conditional Probability
2.5.1 Conditional probability and subjective probability
2.5.2 Conditional probability and cause and effect
2.5.3 Conditional probability and probability of joint events
2.6 Bayes’ Theorem
2.6.1 A challenging problem
2.6.2 A more challenging problem: The three prisoners’ problem
2.7 Random Variables, Average, Variance and Correlation
2.8 Some Specific Distributions
2.8.1 The binomial distribution
2.8.2 The normal distribution
2.8.3 The Poisson distribution
2.9 Generating Functions
2.10 The Law of Large Numbers
3 Elements of Information Theory
3.1 A Qualitative Introduction to Information Theory
3.2 Definition of Shannon’s Information and Its Properties
3.2.1 Properties of the function H for the simplest case of two outcomes
3.2.2 Properties of H for the general case of n outcomes
3.2.3 The consistency property of the missing information (MI)
3.2.4 The case of an infinite number of outcomes
3.3 The Various Interpretations of the Quantity H
3.4 The Assignment of Probabilities by the Maximum Uncertainty Principle
3.5 The Missing Information and the Average Number of Binary Questions Needed to Acquire It
3.6 The False Positive Problem, Revisited
3.7 The Urn Problem, Revisited
4 Transition from the General MI to the Thermodynamic MI
4.1 MI in Binding Systems: One Kind of Information
4.1.1 One ligand on M sites
4.1.2 Two different ligands on M sites
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Tags: Arieh Ben Naim, A Farewell, Statistical Thermodynamics