# A farewell to entropy : statistical thermodynamics based on information : S=logW /

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Author / Creator: | Ben-Naim, Arieh, 1934- |
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Imprint: | Hackensack, N.J. : World Scientific, c2008. |

Description: | xxv, 384 p. : ill. (some col.) ; 23 cm. |

Language: | English |

Subject: | Entropy. Second law of thermodynamics. Statistical thermodynamics. Entropy. Information theory in physics. Second law of thermodynamics. Statistical thermodynamics. |

Format: | Print Book |

URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7198590 |

**Table of Contents:**

- List of Abbreviations
- 2.2.1. The sample space, denoted [Omega]
- Index
- 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
- Preface
- 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
- 1. Introduction
- 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
- 1.1. A Brief History of Temperature and Entropy
- 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
- 4.1.3. Two identical ligands on M sites
- 4.1.4. Generalization to N ligands on M sites
- 4.2. Some Simple Processes in Binding Systems
- 4.2.1. The analog of the expansion process
- 4.2.2. A pure deassimilation process
- 1.2. The Association of Entropy with Disorder
- 4.2.3. Mixing process in a binding system
- 4.2.4. The dependence of MI on the characterization of the system
- 4.3. MI in an Ideal Gas System: Two Kinds of Information. The Sackur-Tetrode Equation
- 4.3.1. The locational MI
- 4.3.2. The momentum MI
- 4.3.3. Combining the locational and the momentum MI
- 4.4. Comments
- 5. The Structure of the Foundations of Statistical Thermodynamics
- 5.1. The Isolated System; The Micro-Canonical Ensemble
- 5.2. System in a Constant Temperature; The Canonical Ensemble
- 1.3. The Association of Entropy with Missing Information
- 5.3. The Classical Analog of the Canonical Partition Function
- 5.4. The Re-interpretation of the Sackur-Tetrode Expression from Informational Considerations
- 5.5. Identifying the Parameter [beta] for an Ideal Gas
- 5.6. Systems at Constant Temperature and Chemical Potential; The Grand Canonical Ensemble
- 5.7. Systems at Constant Temperature and Pressure; The Isothermal Isobaric Ensemble
- 5.8. The Mutual Information due to Intermolecular Interactions
- 6. Some Simple Applications
- 6.1. Expansion of an Ideal Gas
- 6.2. Pure, Reversible Mixing; The First Illusion
- 6.3. Pure Assimilation Process; The Second Illusion
- 2. Elements of Probability Theory
- 6.3.1. Fermi-Dirac (FD) statistics; Fermions
- 6.3.2. Bose-Einstein (BE) statistics; Bosons
- 6.3.3. Maxwell-Boltzmann (MB) statistics
- 6.4. Irreversible Process of Mixing Coupled with Expansion
- 6.5. Irreversible Process of Demixing Coupled with Expansion
- 6.6. Reversible Assimilation Coupled with Expansion
- 6.7. Reflections on the Processes of Mixing and Assimilation
- 6.8. A Pure Spontaneous Deassimilation Process
- 6.9. A Process Involving only Change in the Momentum Distribution
- 6.10. A Process Involving Change in the Intermolecular Interaction Energy
- 2.1. Introduction
- 6.11. Some Baffling Experiments
- 6.12. The Second Law of Thermodynamics
- Appendices
- A. Newton's binomial theorem and some useful identities involving binomial coefficients
- B. The total number of states in the Fermi-Dirac and the Bose-Einstein statistics
- C. Pair and triplet independence between events
- D. Proof of the inequality [vertical bar]R(X, Y)[vertical bar] [less than or equal] 1 for the correlation coefficient
- E. The Stirling approximation
- F. Proof of the form of the function H
- G. The method of Lagrange undetermined multipliers
- 2.2. The Axiomatic Approach
- H. Some inequalities for concave functions
- I. The MI for the continuous case
- J. Identical and indistinguishable (ID) particles
- K. The equivalence of the Boltzmann's and Jaynes' procedures to obtain the fundamental distribution of the canonical ensemble
- L. An alternative derivation of the Sackur-Tetrode equation
- M. Labeling and un-labeling of particles
- N. Replacing a sum by its maximal term
- O. The Gibbs paradox (GP)
- P. The solution to the three prisoners' problem
- References