Mathematical theory of nonequilibrium steady states: on the frontier of probability and dynamical systems
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Series: | Lecture notes in mathematics
1833 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 280 S. |
| ISBN: | 3540206116 |
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| 100 | 1 | |a Jiang, Da-Quan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical theory of nonequilibrium steady states |b on the frontier of probability and dynamical systems |c Da-Quan Jiang ; Min Qian ; Ming-Ping Qian |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a IX, 280 S. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1833 | |
| 650 | 4 | |a Nichtgleichgewichtsstatistik - Stochastischer Prozess - Dynamisches System | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Nonequilibrium statistical mechanics | |
| 650 | 4 | |a Nonequilibrium thermodynamics | |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
0.1 Approach of Stochastic Processes 2
0.2 The Dynamical Systems Approach 7
1 Circulation Distribution, Entropy Production and
Irreversibility of Denumerable Markov Chains 11
1.1 Directed Circuits, Cycles and Passage Functions 13
1.2 The Derived Chain 15
1.3 Circulation Distribution of Recurrent Markov Chains 24
1.4 Irreversibility and Entropy Production 28
1.5 Large Deviations and Fluctuation Theorem 34
1.6 Appendix 42
2 Circulation Distribution, Entropy Production and
Irreversibility of Finite Markov Chains with Continuous
Parameter 45
2.1 Circulation Distribution 47
2.2 Irreversibility and Entropy Production 50
2.3 Large Deviations and Fluctuation Theorem 59
3 General Minimal Diffusion Process: its Construction,
Invariant Measure, Entropy Production and Irreversibility. G7
3.1 Construction of the Minimal Semigroup 69
3.1.1 Resolvent Operators and Minimal Semigroup in a
Bounded Domain 70
3.1.2 Resolvent Operators 72
3.1.3 Banach Space C(R ) and the Minimal Semigroup 74
3.2 Ergodic Stationary Diffusion Process 75
3.2.1 Transition Functions 75
3.2.2 Invariant Functional and Invariant Measure 78
3.2.3 Uniqueness of Invariant Probability Measure 82
VIII Contents
3.2.4 Foguel Alternatives and Ergodicity 83
3.3 Irreversibility and Entropy Production 85
3.3.1 Heuristic Derivation for Entropy Production Rate 85
3.3.2 Reversibility, Symmetry and Zero Entropy Production . 87
4 Measure theoretic Discussion on Entropy Production of
Diffusion Processes and Fluctuation dissipation Theorem .. 93
4.1 Measure theoretic Discussion on Entropy Production of
Diffusions 95
4.1.1 Case of Bounded Coefficients 95
4.1.2 General Case 103
4.2 Drift Velocity, Flux and the Einstein Relation 106
4.2.1 Probabilistic Definition of Drift Velocity and Flux 106
4.2.2 The Einstein Relation 107
4.3 The Green Kubo Formula and Power Spectrum of General
Reversible Markov Processes Ill
4.3.1 Equivalent Conditions for a Markov Process being
Reversible Ill
4.3.2 The Green Kubo Formula 116
4.3.3 Power Spectrum of Reversible Markov Processes 118
5 Entropy Production, Rotation Numbers and Irreversibility
of Diffusion Processes on Manifolds 121
5.1 A Simple Example: Diffusion Processes on a Circle 123
5.2 Lifted Processes and Cameron Martin Girsanov Formula 126
5.3 Irreversibility and Entropy Production 134
5.4 Rotation Numbers and Circulation Decomposition 139
6 On a System of Hyperstable Frequency Locking
Persistence under White Noise 149
6.1 Positive Recurrence 151
6.2 Rotation Numbers 156
7 Entropy Production and Information Gain in Axiom A
Systems 159
7.1 Basic Notions and Results 161
7.1.1 General Thermodynamic Formalism 161
7.1.2 Subshift of Finite Type and Gibbs Measure 162
7.1.3 Axiom A Diffeomorphism 163
7.2 Information Gain 164
7.2.1 Subshift of Finite Type 164
7.2.2 Axiom A Diffeomorphism 169
7.2.2.1 Mixing Case 169
7.2.2.2 Transitive Case 172
7.3 Entropy Production in Axiom A Systems 173
Contents IX
7.4 Large Deviations and Fluctuation Theorem 180
8 Lyapunov Exponents of Hyperbolic Attractors 189
8.1 Basic Facts 192
8.1.1 Oseledec Multiplicative Ergodic Theorem 192
8.1.2 Absolutely Continuous Maps 194
8.1.3 Conditional Measures Given a Measurable Partition ... 194
8.2 Lyapunov Exponents on Stable Manifolds 195
8.3 Case of Uniformly Completely Hyperbolic Attractors 200
8.4 Case of Nonuniformly Completely Hyperbolic Attractors 208
9 Entropy Production, Information Gain and Lyapunov
Exponents of Random Hyperbolic Dynamical Systems 215
9.1 Information Gain in Random Subshifts of Finite Type 217
9.2 Information Gain in Random Hyperbolic Dynamical Systems . 224
9.2.1 Basic Results 224
9.2.2 Mixing Case 228
9.2.3 General Transitive Case 230
9.3 Entropy Production in Random Hyperbolic Dynamical Systems232
9.4 Lyapunov Exponents of Random Hyperbolic Attractors 241
9.5 Appendix 247
References 253
Index 277
|
| any_adam_object | 1 |
| author | Jiang, Da-Quan Qian, Min Qian, Ming-Ping |
| author_facet | Jiang, Da-Quan Qian, Min Qian, Ming-Ping |
| author_role | aut aut aut |
| author_sort | Jiang, Da-Quan |
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| discipline | Mathematik |
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| isbn | 3540206116 |
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| spelling | Jiang, Da-Quan Verfasser aut Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems Da-Quan Jiang ; Min Qian ; Ming-Ping Qian Berlin [u.a.] Springer 2004 IX, 280 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1833 Nichtgleichgewichtsstatistik - Stochastischer Prozess - Dynamisches System Markov processes Nonequilibrium statistical mechanics Nonequilibrium thermodynamics Statistical thermodynamics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Nichtgleichgewichtsstatistik (DE-588)4136220-2 s Stochastischer Prozess (DE-588)4057630-9 s Dynamisches System (DE-588)4013396-5 s DE-604 Qian, Min Verfasser aut Qian, Ming-Ping Verfasser aut Lecture notes in mathematics 1833 (DE-604)BV000676446 1833 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010663430&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jiang, Da-Quan Qian, Min Qian, Ming-Ping Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems Lecture notes in mathematics Nichtgleichgewichtsstatistik - Stochastischer Prozess - Dynamisches System Markov processes Nonequilibrium statistical mechanics Nonequilibrium thermodynamics Statistical thermodynamics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4136220-2 (DE-588)4013396-5 (DE-588)4057630-9 |
| title | Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems |
| title_auth | Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems |
| title_exact_search | Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems |
| title_full | Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems Da-Quan Jiang ; Min Qian ; Ming-Ping Qian |
| title_fullStr | Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems Da-Quan Jiang ; Min Qian ; Ming-Ping Qian |
| title_full_unstemmed | Mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems Da-Quan Jiang ; Min Qian ; Ming-Ping Qian |
| title_short | Mathematical theory of nonequilibrium steady states |
| title_sort | mathematical theory of nonequilibrium steady states on the frontier of probability and dynamical systems |
| title_sub | on the frontier of probability and dynamical systems |
| topic | Nichtgleichgewichtsstatistik - Stochastischer Prozess - Dynamisches System Markov processes Nonequilibrium statistical mechanics Nonequilibrium thermodynamics Statistical thermodynamics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Nichtgleichgewichtsstatistik - Stochastischer Prozess - Dynamisches System Markov processes Nonequilibrium statistical mechanics Nonequilibrium thermodynamics Statistical thermodynamics Nichtgleichgewichtsstatistik Dynamisches System Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010663430&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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