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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2001
|
| Schriftenreihe: | World Scientific lecture notes in physics
v. 66 |
| Schlagworte: | |
| Online-Zugang: | FHN01 URL des Erstveroeffentlichers |
| 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 classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble.Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phase transitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E,N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum.The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum." |
| Beschreibung: | xv, 269 p. ill |
| ISBN: | 9789812798916 |
Internformat
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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 classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble.Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phase transitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E,N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum.The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum." | ||
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Datensatz im Suchindex
| _version_ | 1804178049731657728 |
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| any_adam_object | |
| author | Gross, Dieter H. E. |
| author_facet | Gross, Dieter H. E. |
| author_role | aut |
| author_sort | Gross, Dieter H. E. |
| author_variant | d h e g dhe dheg |
| building | Verbundindex |
| bvnumber | BV044635991 |
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| dewey-full | 536.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 536 - Heat |
| dewey-raw | 536.7 |
| dewey-search | 536.7 |
| dewey-sort | 3536.7 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV044635991 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:48Z |
| institution | BVB |
| isbn | 9789812798916 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030033963 |
| oclc_num | 881298765 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xv, 269 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| series2 | World Scientific lecture notes in physics |
| spelling | Gross, Dieter H. E. Verfasser aut Microcanonical thermodynamics phase transitions in "small" systems Dieter H.E. Gross Singapore World Scientific Pub. Co. c2001 xv, 269 p. ill txt rdacontent c rdamedia cr rdacarrier World Scientific lecture notes in physics v. 66 "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 classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble.Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phase transitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E,N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum.The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum." Statistical thermodynamics Phase transformations (Statistical physics) Mikrokanonische Gesamtheit (DE-588)4444250-6 gnd rswk-swf Thermodynamik (DE-588)4059827-5 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Thermodynamik (DE-588)4059827-5 s Phasenumwandlung (DE-588)4132140-6 s Mikrokanonische Gesamtheit (DE-588)4444250-6 s 1\p DE-604 Statistische Mechanik (DE-588)4056999-8 s 2\p DE-604 Erscheint auch als Druck-Ausgabe 9789810242152 Erscheint auch als Druck-Ausgabe 9810242158 http://www.worldscientific.com/worldscibooks/10.1142/4340#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gross, Dieter H. E. Microcanonical thermodynamics phase transitions in "small" systems Statistical thermodynamics Phase transformations (Statistical physics) Mikrokanonische Gesamtheit (DE-588)4444250-6 gnd Thermodynamik (DE-588)4059827-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| subject_GND | (DE-588)4444250-6 (DE-588)4059827-5 (DE-588)4056999-8 (DE-588)4132140-6 |
| title | Microcanonical thermodynamics 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 Phase transformations (Statistical physics) Mikrokanonische Gesamtheit (DE-588)4444250-6 gnd Thermodynamik (DE-588)4059827-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| topic_facet | Statistical thermodynamics Phase transformations (Statistical physics) Mikrokanonische Gesamtheit Thermodynamik Statistische Mechanik Phasenumwandlung |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4340#t=toc |
| work_keys_str_mv | AT grossdieterhe microcanonicalthermodynamicsphasetransitionsinsmallsystems |