Equidistribution of dynamical systems: time-quantitative second law
"We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For e...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2020
|
| Schriftenreihe: | Fractals and dynamics in mathematics, science, and the arts : theory and applications
v. 7 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For example, what can we say about the typical time evolution of a large system starting from a stage far from equilibrium? What happens in a realistic time scale? The reader's first reaction is probably: What about the famous Second Law (of thermodynamics)? Unfortunately, there are plenty of notorious mathematical problems surrounding the Second Law. (1) How to rigorously define entropy? How to convert the well known intuitions (like "disorder" and "energy spreading") into precise mathematical definitions? (2) How to express the Second Law in forms of a rigorous mathematical theorem? (3) The Second Law is a "soft" qualitative statement about entropy increase, but does not say anything about the necessary time to reach equilibrium. The object of this book is to answer questions (1)-(2)-(3). We rigorously prove a Time-Quantitative Second Law that works on a realistic time scale. As a by product, we clarify the Loschmidt-paradox and the related reversibility/irreversibility paradox"--Publisher's website |
| Beschreibung: | 1 Online-Ressource (xxvi, 421 Seiten) |
| ISBN: | 9789811225567 |
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| 490 | 0 | |a Fractals and dynamics in mathematics, science, and the arts : theory and applications |v v. 7 | |
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Datensatz im Suchindex
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| index_date | 2024-07-03T16:30:25Z |
| indexdate | 2024-07-10T09:03:18Z |
| institution | BVB |
| isbn | 9789811225567 |
| language | English |
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| series2 | Fractals and dynamics in mathematics, science, and the arts : theory and applications |
| spelling | Beck, József Verfasser aut Equidistribution of dynamical systems time-quantitative second law by Jozsef Beck Singapore World Scientific 2020 1 Online-Ressource (xxvi, 421 Seiten) txt rdacontent c rdamedia cr rdacarrier Fractals and dynamics in mathematics, science, and the arts : theory and applications v. 7 "We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For example, what can we say about the typical time evolution of a large system starting from a stage far from equilibrium? What happens in a realistic time scale? The reader's first reaction is probably: What about the famous Second Law (of thermodynamics)? Unfortunately, there are plenty of notorious mathematical problems surrounding the Second Law. (1) How to rigorously define entropy? How to convert the well known intuitions (like "disorder" and "energy spreading") into precise mathematical definitions? (2) How to express the Second Law in forms of a rigorous mathematical theorem? (3) The Second Law is a "soft" qualitative statement about entropy increase, but does not say anything about the necessary time to reach equilibrium. The object of this book is to answer questions (1)-(2)-(3). We rigorously prove a Time-Quantitative Second Law that works on a realistic time scale. As a by product, we clarify the Loschmidt-paradox and the related reversibility/irreversibility paradox"--Publisher's website Dynamics / Mathematical models Dynamics https://www.worldscientific.com/worldscibooks/10.1142/11974#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Beck, József Equidistribution of dynamical systems time-quantitative second law Dynamics / Mathematical models Dynamics |
| title | Equidistribution of dynamical systems time-quantitative second law |
| title_auth | Equidistribution of dynamical systems time-quantitative second law |
| title_exact_search | Equidistribution of dynamical systems time-quantitative second law |
| title_exact_search_txtP | Equidistribution of dynamical systems time-quantitative second law |
| title_full | Equidistribution of dynamical systems time-quantitative second law by Jozsef Beck |
| title_fullStr | Equidistribution of dynamical systems time-quantitative second law by Jozsef Beck |
| title_full_unstemmed | Equidistribution of dynamical systems time-quantitative second law by Jozsef Beck |
| title_short | Equidistribution of dynamical systems |
| title_sort | equidistribution of dynamical systems time quantitative second law |
| title_sub | time-quantitative second law |
| topic | Dynamics / Mathematical models Dynamics |
| topic_facet | Dynamics / Mathematical models Dynamics |
| url | https://www.worldscientific.com/worldscibooks/10.1142/11974#t=toc |
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