A farewell to entropy : statistical thermodynamics based on information : S=logW /
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| Author / Creator: | Ben-Naim, Arieh, 1934- |
|---|---|
| Imprint: | Hackensack, N.J. : World Scientific, ©2008. |
| Description: | 1 online resource (xxv, 384 pages) : illustrations (some color) |
| Language: | English |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11202038 |
Table of Contents:
- 1. Introduction
- A brief history of temperature and entropy
- The association of entropy with disorder
- The association of entropy with missing information
- 2. Elements of probability theory
- Introduction
- The axiomatic approach
- The classical definition
- The relative frequency definition
- Independent events and conditional probability
- Bayes' Theorem
- Random variables, average, variance and correlation
- Some specific distributions
- Generating functions
- The law of large numbers
- 3. Elements of information theory
- A qualitative introduction to information theory
- Definition of Shannon's information and its properties
- The various interpretations of the quantity H
- The assignment of probabilities by the maximum uncertainty principle
- The missing information and the average number of binary questions needed to acquire it
- The false positive problem, revisited
- The urn problem, revisited
- 4. Transition from the general MI to the thermodynamic MI
- MI in binding systems: one kind of information
- Some simple processes in binding systems
- MI in an ideal gas system: two kinds of information. The Sackur-Tetrode Equation
- Comments
- 5. The structure of the foundations of statistical thermodynamics
- The isolated system; the micro-canonical ensemble
- System in a constant temperature; The canonical ensemble
- The classical analog of the canonical partition function
- The re-interpretation of the Sackur-Tetrode expression from informational considerations
- Identifying the parameter ß for an ideal gas
- Systems at constant temperature and chemical potential; The grand canonical ensemble
- Systems at constant temperature and pressure; The isothermal isobaric ensemble
- The mutual information due to intermolecular interactions
- 6. Some simple applications
- Expansion of an ideal gas
- Pure, reversible mixing; The first illusion
- Pure assimilation process; The second illusion
- Irreversible process of demixing coupled with expansion
- Reversible assimilation coupled with expansion
- Reflections on the processes of mixing and assimilation
- A pure spontaneous deassimilation process
- A process involving only change in the momentum distribution
- A process involving change in the intermolecular interaction energy
- Some baffling experiments
- 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 R (X, Y) <̲ 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
- H: Some inequalities for concave functions
- The MI for the continuous case
- J: Identical and indistinguishable (ID) particles
- 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.