Main description:

This is a book about thermodynamics, not history, but it adopts a semi-historical approach in order to highlight different approaches to entropy. The book does not follow a rigid temporal order of events, nor it is meant to be comprehensive. It includes solved examples for a solid understanding. The division into chapters under the names of key players in the development of the field is not intended to separate these individual contributions entirely, but to highlight their different approaches to entropy. This structure helps to provide a different view-point from other text-books on entropy.

Contents:

1 General thermodynamics 1.1 Mechanics 1.2 The First Law: conservation of energy 1.3 The Ideal Gas
2 Carnot and Clausius 2.1 The Carnot cycle 2.2 The Second Law 2.3 The Gibbs free energy G 2.4 The Helmholtz free energy F2.5 Available work 2.6 Maxwell's relations 2.7 The importance of entropy 2.8 Summary
3 Maxwell and Boltzmann 3.1 The Maxwell-Boltzmann distribution 3.2 The relationship between entropy and probability 3.3 Uses of the partition function 3.4 The H theorem 3.5 Early critics of the H theorem 3.6 Modern critics of the H theorem 3.7 Conclusions
4 Gibbs 4.1 General notions 4.2 Phase 4.3 The Liouville theorem 4.4 The canonical distribution 4.5 Analogies with thermodynamics 4.6 Gibbs Entropy 4.7 Variation of energy 4.8 Chemical potential 4.8.1 Small systems 4.9 Summary
5 Partition functions and ensembles 5.1 Microcanonical ensemble 5.2 Canonical ensemble 5.3 Grand canonical ensemble 5.4 Isobaric ensemble 5.5 Molecular partition function 5.6 Distinguishable particles 5.7 Quantum statistics 5.8 Rotational partition function of linear molecules
6 Planck 6.1 Radiation 6.2 Coarse graining 6.3 The Sackur-Tetrode equation 6.4 Gibbs versus Boltzmann 6.5 Entropy is not anthropomorphic
7 Einstein 7.1 Kinetic theory of thermal equilibrium 7.2 The mechanical meaning of Einstein's h 7.3 A mechanical theory of the second law 7.4 The significance of 7.5 Application to radiation 7.6 The entropy of radiation 7.7 Summary
8 Shannon 8.1 Probability and information 8.2 Maximum entropy 8.3 Bayes's theorem 8.4 Maxwell's demon 8.5 Difficulties with Szilard's principle 8.6 Szilard's engine and quantum measurements 8.7 Landauer's principle 8.8 Subjectivity 8.9 The fluctuation theorem 8.10 Summary
9 Nernst 9.1 Chemical potential 9.2 The equilibrium constant 9.3 Fixing a zero point to entropy 9.4 Modern forms of the Third Law 9.5 Attaining absolute zero 9.6 Negative temperatures
10 On Entropy as Mixed-up-ness 10.1 Gibbs's paradox 10.2 Gibbs's paradox from a statistical viewpoint 10.3 von Neumann entropy 10.4 Entropy as information 10.5 Biological systems 10.6 Economics 10.7 Conclusions
11. ProblemsA. Exact differentials and integrating factorsB. Classical mechanicsC. ErgodicityD. Equipartition of energy