Microcanonical thermodynamics :: phase transitions in "small" systems /
Boltzmann's formula S = In[W (E)] defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; New Jersey :
World Scientific,
©2001.
|
| Schriftenreihe: | World Scientific lecture notes in physics ;
v. 66. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Boltzmann's formula S = In[W (E)] defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay - for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and clas. |
| Beschreibung: | 1 online resource (xv, 269 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 249-263) and index. |
| ISBN: | 9789812798916 9812798919 |
Internformat
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| 245 | 1 | 0 | |a Microcanonical thermodynamics : |b phase transitions in "small" systems / |c Dieter H.E. Gross. |
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| 520 | |a Boltzmann's formula S = In[W (E)] defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay - for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and clas. | ||
| 505 | 0 | |a Preface. 0.1. Who is addressed, and why. 0.2. A necessary clarification. 0.3. Acknowledgment -- ch. 1. Introduction. 1.1. Phase transitions and thermodynamics in "small" systems. 1.2. Boltzmann gives the key. 1.3. Micro-canonical thermodynamics describes non-extensive systems. 1.4. Some realistic systems: nuclei and atomic clusters. 1.5. Plan of this book -- ch. 2. The mechanical basis of thermodynamics. 2.1. Basic definitions. 2.2. The thermodynamic limit, the global concavity of s(e, n). 2.3. Phase transitions micro-canonically. 2.4. Second Law of Thermodynamics and Boltzmann's entropy -- ch. 3. Micro-canonical thermodynamics of phase transitions studied in the Potts model. 3.1. Introduction. 3.2. The surface tension in the Potts model. [GEZ50]. 3.3. The topology of the entropy surface S(E, N) for Potts lattice gases [GV99]. 3.4. On the origin of isolated critical points and critical lines -- ch. 4. Liquid-gas transition and surface tension under constant pressure. 4.1. Andersen's constant pressure ensemble. 4.2. Micro-canonical ensemble with given pressure; The enthalpy. 4.3. Liquid-gas transition in realistic metal systems. 4.4. The relation to the method of the Gibbs-ensemble. 4.5. Alternative microscopic methods to calculate the surface tension. 4.6. Criticism and necessary improvements of the computational method. 4.7. Conclusion -- ch. 5. Statistical fragmentation under repulsive forces of long range. 5.1. Introduction. 5.2. Three dimensional stress of long range: the Coulomb force. 5.3. Two dimensional stress of long range: rapidly rotating hot nuclei[BG95b]. 5.4. Conclusion -- ch. 6. The collapse transition in self-gravitating systems. First model-studies. 6.1. 1 -- and 2 -- dim. Hamiltonian Mean Field Model, a caricature of phase transitions under self-gravitation. 6.2. Collapse of non-extensive (gravitating) systems under conserved angular momentum. | |
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| contents | Preface. 0.1. Who is addressed, and why. 0.2. A necessary clarification. 0.3. Acknowledgment -- ch. 1. Introduction. 1.1. Phase transitions and thermodynamics in "small" systems. 1.2. Boltzmann gives the key. 1.3. Micro-canonical thermodynamics describes non-extensive systems. 1.4. Some realistic systems: nuclei and atomic clusters. 1.5. Plan of this book -- ch. 2. The mechanical basis of thermodynamics. 2.1. Basic definitions. 2.2. The thermodynamic limit, the global concavity of s(e, n). 2.3. Phase transitions micro-canonically. 2.4. Second Law of Thermodynamics and Boltzmann's entropy -- ch. 3. Micro-canonical thermodynamics of phase transitions studied in the Potts model. 3.1. Introduction. 3.2. The surface tension in the Potts model. [GEZ50]. 3.3. The topology of the entropy surface S(E, N) for Potts lattice gases [GV99]. 3.4. On the origin of isolated critical points and critical lines -- ch. 4. Liquid-gas transition and surface tension under constant pressure. 4.1. Andersen's constant pressure ensemble. 4.2. Micro-canonical ensemble with given pressure; The enthalpy. 4.3. Liquid-gas transition in realistic metal systems. 4.4. The relation to the method of the Gibbs-ensemble. 4.5. Alternative microscopic methods to calculate the surface tension. 4.6. Criticism and necessary improvements of the computational method. 4.7. Conclusion -- ch. 5. Statistical fragmentation under repulsive forces of long range. 5.1. Introduction. 5.2. Three dimensional stress of long range: the Coulomb force. 5.3. Two dimensional stress of long range: rapidly rotating hot nuclei[BG95b]. 5.4. Conclusion -- ch. 6. The collapse transition in self-gravitating systems. First model-studies. 6.1. 1 -- and 2 -- dim. Hamiltonian Mean Field Model, a caricature of phase transitions under self-gravitation. 6.2. Collapse of non-extensive (gravitating) systems under conserved angular momentum. |
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| dewey-sort | 3536 17 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay - for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and clas.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Preface. 0.1. Who is addressed, and why. 0.2. A necessary clarification. 0.3. Acknowledgment -- ch. 1. Introduction. 1.1. Phase transitions and thermodynamics in "small" systems. 1.2. Boltzmann gives the key. 1.3. Micro-canonical thermodynamics describes non-extensive systems. 1.4. Some realistic systems: nuclei and atomic clusters. 1.5. Plan of this book -- ch. 2. The mechanical basis of thermodynamics. 2.1. Basic definitions. 2.2. The thermodynamic limit, the global concavity of s(e, n). 2.3. Phase transitions micro-canonically. 2.4. Second Law of Thermodynamics and Boltzmann's entropy -- ch. 3. Micro-canonical thermodynamics of phase transitions studied in the Potts model. 3.1. Introduction. 3.2. The surface tension in the Potts model. [GEZ50]. 3.3. The topology of the entropy surface S(E, N) for Potts lattice gases [GV99]. 3.4. On the origin of isolated critical points and critical lines -- ch. 4. Liquid-gas transition and surface tension under constant pressure. 4.1. Andersen's constant pressure ensemble. 4.2. Micro-canonical ensemble with given pressure; The enthalpy. 4.3. Liquid-gas transition in realistic metal systems. 4.4. The relation to the method of the Gibbs-ensemble. 4.5. Alternative microscopic methods to calculate the surface tension. 4.6. Criticism and necessary improvements of the computational method. 4.7. 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| id | ZDB-4-EBA-ocn261340391 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:32Z |
| institution | BVB |
| isbn | 9789812798916 9812798919 |
| language | English |
| oclc_num | 261340391 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 269 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| series | World Scientific lecture notes in physics ; |
| series2 | World Scientific lecture notes in physics ; |
| spelling | Gross, Dieter H. E. https://id.oclc.org/worldcat/entity/E39PCjH6MB9TpCRjWJdDvf8CFC http://id.loc.gov/authorities/names/no2001055815 Microcanonical thermodynamics : phase transitions in "small" systems / Dieter H.E. Gross. Phase transitions in "small" systems Singapore ; New Jersey : World Scientific, ©2001. 1 online resource (xv, 269 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific lecture notes in physics ; v. 66 Includes bibliographical references (pages 249-263) and index. Print version record. Boltzmann's formula S = In[W (E)] defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay - for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and clas. Preface. 0.1. Who is addressed, and why. 0.2. A necessary clarification. 0.3. Acknowledgment -- ch. 1. Introduction. 1.1. Phase transitions and thermodynamics in "small" systems. 1.2. Boltzmann gives the key. 1.3. Micro-canonical thermodynamics describes non-extensive systems. 1.4. Some realistic systems: nuclei and atomic clusters. 1.5. Plan of this book -- ch. 2. The mechanical basis of thermodynamics. 2.1. Basic definitions. 2.2. The thermodynamic limit, the global concavity of s(e, n). 2.3. Phase transitions micro-canonically. 2.4. Second Law of Thermodynamics and Boltzmann's entropy -- ch. 3. Micro-canonical thermodynamics of phase transitions studied in the Potts model. 3.1. Introduction. 3.2. The surface tension in the Potts model. [GEZ50]. 3.3. The topology of the entropy surface S(E, N) for Potts lattice gases [GV99]. 3.4. On the origin of isolated critical points and critical lines -- ch. 4. Liquid-gas transition and surface tension under constant pressure. 4.1. Andersen's constant pressure ensemble. 4.2. Micro-canonical ensemble with given pressure; The enthalpy. 4.3. Liquid-gas transition in realistic metal systems. 4.4. The relation to the method of the Gibbs-ensemble. 4.5. Alternative microscopic methods to calculate the surface tension. 4.6. Criticism and necessary improvements of the computational method. 4.7. Conclusion -- ch. 5. Statistical fragmentation under repulsive forces of long range. 5.1. Introduction. 5.2. Three dimensional stress of long range: the Coulomb force. 5.3. Two dimensional stress of long range: rapidly rotating hot nuclei[BG95b]. 5.4. Conclusion -- ch. 6. The collapse transition in self-gravitating systems. First model-studies. 6.1. 1 -- and 2 -- dim. Hamiltonian Mean Field Model, a caricature of phase transitions under self-gravitation. 6.2. Collapse of non-extensive (gravitating) systems under conserved angular momentum. Statistical thermodynamics. http://id.loc.gov/authorities/subjects/sh85127576 Phase transformations (Statistical physics) http://id.loc.gov/authorities/subjects/sh85100646 Thermodynamique statistique. Transitions de phase. SCIENCE Mechanics Thermodynamics. bisacsh Phase transformations (Statistical physics) fast Statistical thermodynamics fast Termodinâmica. larpcal has work: Microcanonical thermodynamics (Text) https://id.oclc.org/worldcat/entity/E39PCGKHMWcDRWbVbwBbYVHPV3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Gross, Dieter H.E. Microcanonical thermodynamics. Singapore ; New Jersey : World Scientific, ©2001 9810242158 9789810242152 (DLC) 2002275558 (OCoLC)47215466 World Scientific lecture notes in physics ; v. 66. http://id.loc.gov/authorities/names/n84715132 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235920 Volltext |
| spellingShingle | Gross, Dieter H. E. Microcanonical thermodynamics : phase transitions in "small" systems / World Scientific lecture notes in physics ; Preface. 0.1. Who is addressed, and why. 0.2. A necessary clarification. 0.3. Acknowledgment -- ch. 1. Introduction. 1.1. Phase transitions and thermodynamics in "small" systems. 1.2. Boltzmann gives the key. 1.3. Micro-canonical thermodynamics describes non-extensive systems. 1.4. Some realistic systems: nuclei and atomic clusters. 1.5. Plan of this book -- ch. 2. The mechanical basis of thermodynamics. 2.1. Basic definitions. 2.2. The thermodynamic limit, the global concavity of s(e, n). 2.3. Phase transitions micro-canonically. 2.4. Second Law of Thermodynamics and Boltzmann's entropy -- ch. 3. Micro-canonical thermodynamics of phase transitions studied in the Potts model. 3.1. Introduction. 3.2. The surface tension in the Potts model. [GEZ50]. 3.3. The topology of the entropy surface S(E, N) for Potts lattice gases [GV99]. 3.4. On the origin of isolated critical points and critical lines -- ch. 4. Liquid-gas transition and surface tension under constant pressure. 4.1. Andersen's constant pressure ensemble. 4.2. Micro-canonical ensemble with given pressure; The enthalpy. 4.3. Liquid-gas transition in realistic metal systems. 4.4. The relation to the method of the Gibbs-ensemble. 4.5. Alternative microscopic methods to calculate the surface tension. 4.6. Criticism and necessary improvements of the computational method. 4.7. Conclusion -- ch. 5. Statistical fragmentation under repulsive forces of long range. 5.1. Introduction. 5.2. Three dimensional stress of long range: the Coulomb force. 5.3. Two dimensional stress of long range: rapidly rotating hot nuclei[BG95b]. 5.4. Conclusion -- ch. 6. The collapse transition in self-gravitating systems. First model-studies. 6.1. 1 -- and 2 -- dim. Hamiltonian Mean Field Model, a caricature of phase transitions under self-gravitation. 6.2. Collapse of non-extensive (gravitating) systems under conserved angular momentum. Statistical thermodynamics. http://id.loc.gov/authorities/subjects/sh85127576 Phase transformations (Statistical physics) http://id.loc.gov/authorities/subjects/sh85100646 Thermodynamique statistique. Transitions de phase. SCIENCE Mechanics Thermodynamics. bisacsh Phase transformations (Statistical physics) fast Statistical thermodynamics fast Termodinâmica. larpcal |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85127576 http://id.loc.gov/authorities/subjects/sh85100646 |
| title | Microcanonical thermodynamics : phase transitions in "small" systems / |
| title_alt | Phase transitions in "small" systems |
| title_auth | Microcanonical thermodynamics : phase transitions in "small" systems / |
| title_exact_search | Microcanonical thermodynamics : phase transitions in "small" systems / |
| title_full | Microcanonical thermodynamics : phase transitions in "small" systems / Dieter H.E. Gross. |
| title_fullStr | Microcanonical thermodynamics : phase transitions in "small" systems / Dieter H.E. Gross. |
| title_full_unstemmed | Microcanonical thermodynamics : phase transitions in "small" systems / Dieter H.E. Gross. |
| title_short | Microcanonical thermodynamics : |
| title_sort | microcanonical thermodynamics phase transitions in small systems |
| title_sub | phase transitions in "small" systems / |
| topic | Statistical thermodynamics. http://id.loc.gov/authorities/subjects/sh85127576 Phase transformations (Statistical physics) http://id.loc.gov/authorities/subjects/sh85100646 Thermodynamique statistique. Transitions de phase. SCIENCE Mechanics Thermodynamics. bisacsh Phase transformations (Statistical physics) fast Statistical thermodynamics fast Termodinâmica. larpcal |
| topic_facet | Statistical thermodynamics. Phase transformations (Statistical physics) Thermodynamique statistique. Transitions de phase. SCIENCE Mechanics Thermodynamics. Statistical thermodynamics Termodinâmica. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235920 |
| work_keys_str_mv | AT grossdieterhe microcanonicalthermodynamicsphasetransitionsinsmallsystems AT grossdieterhe phasetransitionsinsmallsystems |