Approaches to Entropy (eBook)

Jeremy R. H. Tame is currently a professor at the Drug Design Laboratory at Yokohama City University in Japan. After graduating from Cambridge University in England, he moved to the MRC Laboratory of Molecular Biology. Following a short period of work with Nobel Prize winner Max Perutz, he joined Kiyoshi Nagai’s group. His group focuses on biophysical studies of how proteins fold and function. His other research interests include x-ray crystallography, protein design and thermodynamics of protein–ligand binding.

1General thermodynamics 1.1Mechanics 1.2The First Law: conservation of energy 1.3     The Ideal Gas 2Carnot and Clausius 2.1The Carnot cycle 2.2The Second Law 2.3The Gibbs free energy G 2.4The Helmholtz free energy F2.5Available work 2.6Maxwell’s  relations 2.7The importance of entropy 2.8Summary 3Maxwell and Boltzmann 3.1The  Maxwell-Boltzmann  distribution 3.2The relationship between entropy and probability 3.3Uses of the partition function 3.4The H theorem 3.5Early critics of the H theorem 3.6Modern critics of the H theorem 3.7   Conclusions 4Gibbs 4.1General notions 4.2Phase 4.3The Liouville theorem 4.4The canonical distribution 4.5Analogies with thermodynamics 4.6Gibbs Entropy 4.7Variation of energy 4.8Chemical potential 4.8.1     Small systems 4.9Summary 5Partition functions and ensembles 5.1Microcanonical ensemble 5.2Canonical  ensemble 5.3Grand canonical ensemble 5.4Isobaric ensemble 5.5Molecular partition function 5.6Distinguishable particles 5.7Quantum statistics 5.8Rotational partition function of linear molecules6Planck 6.1Radiation 6.2Coarse graining 6.3The Sackur-Tetrode equation 6.4Gibbs versus Boltzmann 6.5Entropy is not anthropomorphic 7Einstein 7.1Kinetic theory of thermal equilibrium 7.2The mechanical meaning of Einstein’s h 7.3A mechanical theory of the second law 7.4The significance of κ 7.5Application to radiation 7.6The entropy of radiation 7.7Summary 8Shannon 8.1Probability and information 8.2Maximum entropy 8.3Bayes’s theorem 8.4Maxwell’s  demon 8.5Difficulties with Szilard’s principle 8.6Szilard’s engine and quantum measurements 8.7Landauer’s principle 8.8Subjectivity 8.9The fluctuation theorem 8.10  Summary 9Nernst 9.1Chemical potential 9.2The equilibrium constant 9.3Fixing a zero point to entropy 9.4Modern forms of the Third Law 9.5Attaining absolute zero 9.6Negative temperatures 10On Entropy as Mixed-up-ness 10.1Gibbs’s paradox 10.2Gibbs’s paradox from a statistical viewpoint 10.3von Neumann entropy 10.4Entropy as information 10.5Biological systems 10.6Economics 10.7Conclusions11. ProblemsA.Exact differentials and integrating factorsB.Classical mechanicsC.ErgodicityD.Equipartition of energy