Chaos and coarse graining in statistical mechanics:
While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents th...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2008
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| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (x, 268 pages) |
| ISBN: | 9780511535291 |
| DOI: | 10.1017/CBO9780511535291 |
Staff View
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Basic concepts of dynamical systems theory -- Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond -- Coarse graining, entropies and Lyapunov exponents at work -- Foundation of statistical mechanics and dynamical systems -- On the origin of irreversibility -- The role of chaos in non-equilibrium statistical mechanics -- Coarse-graining equations in complex systems -- Renormalization-group approaches | |
| 520 | |a While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos | ||
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| author_facet | Castiglione, Patrizia 1968- |
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| contents | Basic concepts of dynamical systems theory -- Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond -- Coarse graining, entropies and Lyapunov exponents at work -- Foundation of statistical mechanics and dynamical systems -- On the origin of irreversibility -- The role of chaos in non-equilibrium statistical mechanics -- Coarse-graining equations in complex systems -- Renormalization-group approaches |
| ctrlnum | (ZDB-20-CBO)CR9780511535291 (OCoLC)699133669 (DE-599)BVBBV043944837 |
| dewey-full | 003/.857 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.857 |
| dewey-search | 003/.857 |
| dewey-sort | 13 3857 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik |
| doi_str_mv | 10.1017/CBO9780511535291 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:39:22Z |
| institution | BVB |
| isbn | 9780511535291 |
| language | English |
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| spelling | Castiglione, Patrizia 1968- Verfasser aut Chaos and coarse graining in statistical mechanics Patrizia Castiglione [and three others] Chaos & Coarse Graining in Statistical Mechanics Cambridge Cambridge University Press 2008 1 online resource (x, 268 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Basic concepts of dynamical systems theory -- Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond -- Coarse graining, entropies and Lyapunov exponents at work -- Foundation of statistical mechanics and dynamical systems -- On the origin of irreversibility -- The role of chaos in non-equilibrium statistical mechanics -- Coarse-graining equations in complex systems -- Renormalization-group approaches While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos Chaotic behavior in systems Dynamics Statistical mechanics Mathematical statistics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Statistische Mechanik (DE-588)4056999-8 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-89593-4 https://doi.org/10.1017/CBO9780511535291 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Castiglione, Patrizia 1968- Chaos and coarse graining in statistical mechanics Basic concepts of dynamical systems theory -- Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond -- Coarse graining, entropies and Lyapunov exponents at work -- Foundation of statistical mechanics and dynamical systems -- On the origin of irreversibility -- The role of chaos in non-equilibrium statistical mechanics -- Coarse-graining equations in complex systems -- Renormalization-group approaches Chaotic behavior in systems Dynamics Statistical mechanics Mathematical statistics Statistische Mechanik (DE-588)4056999-8 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4316104-2 |
| title | Chaos and coarse graining in statistical mechanics |
| title_alt | Chaos & Coarse Graining in Statistical Mechanics |
| title_auth | Chaos and coarse graining in statistical mechanics |
| title_exact_search | Chaos and coarse graining in statistical mechanics |
| title_full | Chaos and coarse graining in statistical mechanics Patrizia Castiglione [and three others] |
| title_fullStr | Chaos and coarse graining in statistical mechanics Patrizia Castiglione [and three others] |
| title_full_unstemmed | Chaos and coarse graining in statistical mechanics Patrizia Castiglione [and three others] |
| title_short | Chaos and coarse graining in statistical mechanics |
| title_sort | chaos and coarse graining in statistical mechanics |
| topic | Chaotic behavior in systems Dynamics Statistical mechanics Mathematical statistics Statistische Mechanik (DE-588)4056999-8 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Chaotic behavior in systems Dynamics Statistical mechanics Mathematical statistics Statistische Mechanik Chaotisches System |
| url | https://doi.org/10.1017/CBO9780511535291 |
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