A farewell to entropy: statistical thermodynamics based on information : S=logW
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, N.J.
World Scientific
c2008
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 373-379) and index 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 |
| Beschreibung: | 1 Online-Ressource (xxv, 384 p.) |
| ISBN: | 9789812707062 9789812790736 9812707069 981279073X |
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| 500 | |a 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 -- | ||
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| author | Ben-Naim, Arieh |
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| dewey-ones | 536 - Heat |
| dewey-raw | 536/.73 |
| dewey-search | 536/.73 |
| dewey-sort | 3536 273 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:08Z |
| institution | BVB |
| isbn | 9789812707062 9789812790736 9812707069 981279073X |
| language | English |
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| spelling | Ben-Naim, Arieh Verfasser aut A farewell to entropy statistical thermodynamics based on information : S=logW Arieh Ben-Naim S=logW Hackensack, N.J. World Scientific c2008 1 Online-Ressource (xxv, 384 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 373-379) and index 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 SCIENCE / Mechanics / Thermodynamics bisacsh Entropy fast Second law of thermodynamics fast Statistical thermodynamics fast Entropy Second law of thermodynamics Statistical thermodynamics Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Entropie Informationstheorie (DE-588)4743861-7 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 s Entropie Informationstheorie (DE-588)4743861-7 s 1\p DE-604 Erscheint auch als Druck-Ausgabe, Paperback 978-981-270-707-9 Erscheint auch als Druck-Ausgabe, Paperback 981-270-707-7 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=236065 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ben-Naim, Arieh A farewell to entropy statistical thermodynamics based on information : S=logW SCIENCE / Mechanics / Thermodynamics bisacsh Entropy fast Second law of thermodynamics fast Statistical thermodynamics fast Entropy Second law of thermodynamics Statistical thermodynamics Statistische Thermodynamik (DE-588)4126251-7 gnd Entropie Informationstheorie (DE-588)4743861-7 gnd |
| subject_GND | (DE-588)4126251-7 (DE-588)4743861-7 |
| title | A farewell to entropy statistical thermodynamics based on information : S=logW |
| title_alt | S=logW |
| title_auth | A farewell to entropy statistical thermodynamics based on information : S=logW |
| title_exact_search | A farewell to entropy statistical thermodynamics based on information : S=logW |
| title_full | A farewell to entropy statistical thermodynamics based on information : S=logW Arieh Ben-Naim |
| title_fullStr | A farewell to entropy statistical thermodynamics based on information : S=logW Arieh Ben-Naim |
| title_full_unstemmed | A farewell to entropy statistical thermodynamics based on information : S=logW Arieh Ben-Naim |
| title_short | A farewell to entropy |
| title_sort | a farewell to entropy statistical thermodynamics based on information s logw |
| title_sub | statistical thermodynamics based on information : S=logW |
| topic | SCIENCE / Mechanics / Thermodynamics bisacsh Entropy fast Second law of thermodynamics fast Statistical thermodynamics fast Entropy Second law of thermodynamics Statistical thermodynamics Statistische Thermodynamik (DE-588)4126251-7 gnd Entropie Informationstheorie (DE-588)4743861-7 gnd |
| topic_facet | SCIENCE / Mechanics / Thermodynamics Entropy Second law of thermodynamics Statistical thermodynamics Statistische Thermodynamik Entropie Informationstheorie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=236065 |
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