Quantum thermodynamics: emergence of thermodynamic behavior within composite quantum systems
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
[2009]
|
| Edition: | 2. Edition |
| Series: | Lecture notes in physics
784 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVI, 346 Seiten Diagramme |
| ISBN: | 9783540705093 9783642260995 |
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Record in the Search Index
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| adam_text | Titel: Quantum thermodynamics
Autor: Gemmer, Jochen
Jahr: 2009
Contents
Part I Background
1 Introduction .................................................. 3
References..................................................... g
2 Basics of Quantum Mechanics .................................. 7
2.1 Introductory Remarks...................................... 7
2.2 Operator Representations................................... 8
2.2.1 Transition Operators................................ 8
2.2.2 Pauli Operators.................................... 9
2.2.3 State Representation................................ 9
2.2.4 Purity and von Neumann Entropy..................... 11
2.2.5 Bipartite Systems.................................. 12
2.2.6 Multipartite Systems............................... 14
2.3 Dynamics................................................ 15
2.4 Invariants ................................................ 17
2.5 Time-Dependent Perturbation Theory......................... 19
2.5.1 Interaction Picture................................. 19
2.5.2 Series Expansion .................................. 20
References..................................................... 22
3 Basics of Thermodynamics and Statistics......................... 23
3.1 Phenomenological Thermodynamics.......................... 23
3.1.1 Basic Definitions .................................. 23
3.1.2 Fundamental Laws................................. 24
3.1.3 Gibbsian Fundamental Form......................... 28
3.1.4 Thermodynamic Potentials.......................... 29
3.2 Linear Non-equilibrium Thermodynamics..................... 30
3.3 Statistics................................................. 32
3.3.1 Boltzmann s Principle, A Priori Postulate.............. 33
3.3.2 Microcanonical Ensemble........................... 34
Contents
3.3.3 Statistical Entropy, Maximum Principle ............... 36
References..................................................... Jy
Brief Review of Pertinent Concepts .............................. 41
4.1 Boltzmann s Equation and //-Theorem....................... 42
4.2 Ergodicity................................................ 46
4.3 Ensemble Approach ....................................... 47
4.4 Macroscopic Cell Approach................................. 48
4.5 The Problem of Adiabatic State Change....................... 51
4.6 Shannon Entropy, Jaynes Principle .......................... 53
4.7 Time-Averaged Density Matrix Approach..................... 54
4.8 Open System Approach and Master Equation.................. 55
References..................................................... 61
Part II Equilibrium
5 The Program for the Foundation of Thermodynamics............... 65
5.1 Basic Checklist: Equilibrium Thermodynamics................. 66
5.2 Supplementary Checklist: Quantum Mechanical Versus Classical
Aspects.................................................. 68
Reference...................................................... 68
6 Outline of the Present Approach................................. 69
6.1 Typicality and Dynamics ................................... 69
6.1.1 On the Analysis of Quantum Typicality................ 73
6.2 Compound Systems, Entropy, and Entanglement................ 74
6.3 Fundamental and Subjective Lack of Knowledge............... 75
References..................................................... 76
7 Dynamics and Averages in Hilbert Space ......................... 77
7.1 Representation of Hilbert Space.............................. 77
7.2 Dynamics in Hilbert Space.................................. 78
7.3 Hilbert Space Average and Variance.......................... 81
References..................................................... 83
8 Typicality of Observables and States ............................. 85
8.1 A Class of Accessible Regions............................... 85
8.2 Hilbert Space Average of Observables........................ 87
8.3 Hilbert Space Variance of Observables........................ 89
8.4 Hilbert Space Averages of Distances Between States............ 91
References............................................. 93
Contents xiii
9 System and Environment........................................ 95
9.1 Partition of the System and Pertinent Notation.................. 95
9.2 Comment on Bipartite Systems and Physical Scenarios.......... 98
9.3 Weak Coupling and Corresponding Accessible Regions..........100
9.3.1 Microcanonical Conditions..........................102
9.3.2 Energy Exchange Conditions........................103
References.....................................................105
10 The Typical Reduced State of the System .........................107
10.1 Reduced State and Typicality................................107
10.2 Microcanonical Conditions..................................110
10.2.1 Microcanonical Average State .......................110
10.2.2 Typicality of the Microcanonical Average State.........Ill
10.3 Energy Exchange Conditions................................113
10.3.1 Energy Exchange Average State......................113
10.3.2 Typicality of the Energy Exchange Average State.......114
10.4 Canonical Conditions......................................115
10.5 Beyond Weak Coupling....................................116
References.....................................................117
11 Entanglement, Correlations, and Local Entropy...................119
11.1 Entanglement, Correlations, and Relaxation....................119
11.2 Entropy and Purity......................................... 23
References.....................................................126
12 Generic Spectra of Large Systems ...............................I29
12.1 The Extensivity of Entropy..................................129
12.2 Spectra of Modular Systems.................................131
12.3 Entropy of an Ideal Gas ....................................134
12.4 Environmental Spectra and Boltzmann Distribution.............136
12.5 Beyond the Boltzmann Distribution? .........................I37
References.....................................................
13 Temperature ..................................................^
13.1 Definition of Spectral Temperature............•.............. ™
13.2 The Equality of Spectral Temperatures in Equilibrium...........I4
13.3 Spectral Temperature as the Derivative of Energy with Respect to
..................................................
p..................................................l44
13.3.1 Contact with a Hotter System........................ *~
13.3.2 Energy Deposition.................................|4g
References.....................................................
149
14 Pressure and Adiabatic Processes................................
14.1 On the Concept of Adiabatic Processes........................^
References.....................................................
xvi Contents
24.1.1 LEMBAS Scenario.................................275
24.1.2 Applications......................................279
24.1.3 Remarks..........................................281
24.2 Fluctuations ofWork.......................................282
24.2.1 Microcanonical Coupling...........................284
24.2.2 Canonical Coupling: Constant Interaction Energy.......286
24.2.3 Canonical Coupling: High-Temperature Limit..........286
24.2.4 Numerical Verification..............................288
References.....................................................289
25 Quantum Thermodynamic Processes..............................291
25.1 Model of Control..........................................291
25.2 Quasi-static Limit.........................................293
25.2.1 Thermodynamic Quantities..........................293
25.2.2 Otto Cycle........................................295
25.2.3 Carnot Cycle......................................297
25.2.4 Continuum Limit of the Particle in a Box..............299
25.3 Processes Beyond the Quasi-static Limit......................300
25.3.1 Solution of the Relaxation Equation...................302
25.3.2 Otto Cycle at Finite Velocity.........................303
25.3.3 Carnot Cycle at Finite Velocity.......................308
References.....................................................313
A Hyperspheres .................................................315
A.I Averaging of Functions over Hyperspheres....................315
B General Hilbert Space Averages and Variances....................319
B.I Hilbert Space Averages of Polynomial Terms..................319
B.2 Hilbert Space Variance of an Observable......................321
C Special Hilbert Space Averages and Variances.....................325
C. 1 General Distances Between States............................325
C.2 Microcanonical Hilbert Space Averages.......................326
C.3 Microcanonical Hilbert Space Variances ......................327
C.4 Energy Exchange Hilbert Space Averages.....................329
C.5 Energy Exchange Hilbert Space Variance......................330
D Power of a Function............................................333
E Local Temperature Conditions for a Spin Chain...................335
References......................................... 338
Index
339
|
| any_adam_object | 1 |
| author | Gemmer, Jochen Michel, Mathias 1975- Mahler, Günter 1945-2016 |
| author_GND | (DE-588)124588638 (DE-588)132245094 (DE-588)108184501 |
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| dewey-search | 536.7 530.12 |
| dewey-sort | 3536.7 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 2. Edition |
| format | Book |
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| spelling | Gemmer, Jochen Verfasser (DE-588)124588638 aut Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems J. Gemmer ; M. Michel ; G. Mahler 2. Edition Berlin ; Heidelberg Springer [2009] @2009 XVI, 346 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 784 Hier auch später erschienene, unveränderte Nachdrucke Quantum theory Quantenmechanisches System - Thermodynamik Quantentheorie Thermodynamik (DE-588)4059827-5 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 s Thermodynamik (DE-588)4059827-5 s DE-604 Michel, Mathias 1975- Verfasser (DE-588)132245094 aut Mahler, Günter 1945-2016 Verfasser (DE-588)108184501 aut Lecture notes in physics 784 (DE-604)BV000003166 784 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017322407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gemmer, Jochen Michel, Mathias 1975- Mahler, Günter 1945-2016 Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems Lecture notes in physics Quantum theory Quantenmechanisches System - Thermodynamik Quantentheorie Thermodynamik (DE-588)4059827-5 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| subject_GND | (DE-588)4059827-5 (DE-588)4300046-0 |
| title | Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems |
| title_auth | Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems |
| title_exact_search | Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems |
| title_full | Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems J. Gemmer ; M. Michel ; G. Mahler |
| title_fullStr | Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems J. Gemmer ; M. Michel ; G. Mahler |
| title_full_unstemmed | Quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems J. Gemmer ; M. Michel ; G. Mahler |
| title_short | Quantum thermodynamics |
| title_sort | quantum thermodynamics emergence of thermodynamic behavior within composite quantum systems |
| title_sub | emergence of thermodynamic behavior within composite quantum systems |
| topic | Quantum theory Quantenmechanisches System - Thermodynamik Quantentheorie Thermodynamik (DE-588)4059827-5 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| topic_facet | Quantum theory Quantenmechanisches System - Thermodynamik Quantentheorie Thermodynamik Quantenmechanisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017322407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
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