Contents -- List of Abbreviations -- Preface -- 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 -- 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 -- 3.2.4.1 The uniform distribution of locations -- 3.2.4.2 The normal distribution of velocities or momenta -- 3.2.4.3 The Boltzmann distribution -- 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 -- 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 -- 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 -- 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 β 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 -- 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 -- 6.11 Some Baffing 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