Nonequilibrium statistical physics of small systems: fluctuation relations and beyond
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2013
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| Series: | Reviews of Nonlinear Dynamics and Complexity
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXVIII, 418 S. Ill., graph. Darst. 240 mm x 170 mm |
| ISBN: | 9783527410941 9783527658701 |
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| 245 | 1 | 0 | |a Nonequilibrium statistical physics of small systems |b fluctuation relations and beyond |c ed. by Rainer Klages ... |
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2013 | |
| 300 | |a XXVIII, 418 S. |b Ill., graph. Darst. |c 240 mm x 170 mm | ||
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| 490 | 0 | |a Reviews of Nonlinear Dynamics and Complexity | |
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Record in the Search Index
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IMAGE 1
V
CONTENTS
PREFACE XIII
LIST O F CONTRIBUTORS XVII COLOR PLATES XXIII
PART I FLUCTUATION RELATIONS 1
1 FLUCTUATION RELATIONS: A PEDAGOGICAL OVERVIEW 3
RICHARD SPINNEY AND IAN FORD 1.1 PRELIMINARIES 3
1.2 ENTROPY A N D THE SECOND LAW 5
1.3 STOCHASTIC DYNAMICS 8
1.3.1 MASTER EQUATIONS 8
1.3.2 KRAMERS-MOYAL AND FOKKER-PLANCK EQUATIONS 9 1.3.3
ORNSTEIN-UHLENBECK PROCESS 11
1.4 ENTROPY GENERATION AND STOCHASTIC IRREVERSIBILITY 13 1.4.1
REVERSIBILITY O F A STOCHASTIC TRAJECTORY 13 1.5 ENTROPY PRODUCTION I N
THE OVERDAMPED LIMIT 21
1.6 ENTROPY, STATIONARITY, A N D DETAILED BALANCE 25
1.7 A GENERAL FLUCTUATION THEOREM 2 7
1.7.1 WORK RELATIONS 3 0
1.7.1.1 THE CROOKS WORK RELATION AND JARZYNSKI EQUALITY 31 1.7.2
FLUCTUATION RELATIONS FOR MECHANICAL WORK 34 1.7.3 FLUCTUATION THEOREMS
FOR ENTROPY PRODUCTION 36 1.8 FURTHER RESULTS 3 7
1.8.1 ASYMPTOTIC FLUCTUATION THEOREMS 37 1.8.2 GENERALIZATIONS A N D
CONSIDERATION O F ALTERNATIVE DYNAMICS 39 1.9 FLUCTUATION RELATIONS FOR
REVERSIBLE DETERMINISTIC SYSTEMS 41 1.10 EXAMPLES O F THE FLUCTUATION
RELATIONS I N ACTION 45 1.10.1 HARMONIC OSCILLATOR SUBJECT TO A STEP
CHANGE I N SPRING CONSTANT 45 1.10.2 SMOOTHLY SQUEEZED HARMONIC
OSCILLATOR 4 9 1.10.3 A SIMPLE NONEQUILIBRIUM STEADY STATE 52 1.11 FINAL
REMARKS 54
REFERENCES 5 5
HTTP://D-NB.INFO/1025272048
IMAGE 2
V I CONTENTS
2 FLUCTUATION RELATIONS AND THE FOUNDATIONS O F STATISTICAL
THERMODYNAMICS: A DETERMINISTIC APPROACH AND NUMERICAL DEMONSTRATION 5 7
JAMES C. REID, STEPHEN R. WILLIAMS, DEBRA J. SEARLES, LAMBERTO RONDONI,
AND DENIS J. EVANS 2.1 INTRODUCTION 5 7
2.2 THE RELATIONS 58
2.3 PROOF O F BOLTZMANN'S POSTULATE O F EQUAL A PRIORI PROBABILITIES 62
2.4 NONEQUILIBRIUM FREE ENERGY RELATIONS 6 7
2.5 SIMULATIONS AND RESULTS 69
2.6 RESULTS DEMONSTRATING THE FLUCTUATION RELATIONS 74 2.7 CONCLUSION 80
REFERENCES 81
3 FLUCTUATION RELATIONS IN SMALL SYSTEMS: EXACT RESULTS FROM T H E
DETERMINISTIC APPROACH 83 LAMBERTO RONDONI AND O.C.JEPPS 3.1 MOTIVATION
84
3.1.1 WHY FLUCTUATIONS? 85
* 3.1.2 NONEQUILIBRIUM MOLECULAR DYNAMICS 86 3.1.3 THE DISSIPATION
FUNCTION 89
3.1.4 FLUCTUATION RELATIONS: THE NEED FOR CLARIFICATION 92 3.2 FORMAL
DEVELOPMENT 94
3.2.1 TRANSIENT RELATIONS 94
3.2.2 WORK RELATIONS: JARZYNSKI 96
3.2.3 ASYMPTOTIC RESULTS 98
3.2.4 EXTENDING TOWARD THE STEADY STATE 101 3.2.5 THE GALLAVOTTI-COHEN
APPROACH 105 3.3 DISCUSSION 108
3.4 CONCLUSIONS 110
REFERENCES 111
4 MEASURING OUT-OF-EQUILIBRIUM FLUCTUATIONS 115 L. BELLON, J. R. GOMEZ-
SOLANO, A. PETROSYAN, AND SERGIO CILIBERTO 4.1 INTRODUCTION 115
4.2 WORK AND HEAT FLUCTUATIONS I N THE HARMONIC OSCILLATOR 116 4.2.1 THE
EXPERIMENTAL SETUP 116
4.2.2 THE EQUATION O F MOTION 117
4.2.2.1 EQUILIBRIUM 117
4.2.3 NONEQUILIBRIUM STEADY STATE: SINUSOIDAL FORCING 118 4.2.4 ENERGY
BALANCE 119
4.2.5 HEAT FLUCTUATIONS 120
4.3 FLUCTUATION THEOREM 121
4.3.1 FTS FOR GAUSSIAN VARIABLES 122
IMAGE 3
CONTENTS I V I I
4.3.2 FTS FOR W T A N D Q R M E A S U R E D I N THE HARMONIC
OSCILLATOR 123
4.3.3 COMPARISON WITH THEORY 125
4.3.4 TRAJECTORY-DEPENDENT ENTROPY 125 4.4 THE NONLINEAR CASE:
STOCHASTIC RESONANCE 128
4.5 RANDOM DRIVING 132
4.5.1 COLLOIDAL PARTICLE I N A N OPTICAL TRAP 132 4.5.2 AFM CANTILEVER
136
4.5.3 FLUCTUATION RELATIONS FAR FROM EQUILIBRIUM 139 4.5.4 CONCLUSIONS O
N RANDOMLY DRIVEN SYSTEMS 142 4.6 APPLICATIONS O F FLUCTUATION THEOREMS
142
4.6.1 FLUCTUATION-DISSIPATION RELATIONS FOR NESS 143 4.6.1.1 HATANO-SASA
RELATION A N D FLUCTUATION-DISSIPATION AROUND NESS 144 4.6.1.2 BROWNIAN
PARTICLE I N A TOROIDAL OPTICAL TRAP 144 4.6.2 GENERALIZED
FLUCTUATION-DISSIPATION RELATION 146
4.6.2.1 STATISTICAL ERROR 146
4.6.2.2 EFFECT O F THE INITIAL SAMPLED CONDITION 147 4.6.2.3
EXPERIMENTAL TEST 149 4.6.3 DISCUSSION O N FDT 149
4.7 SUMMARY A N D CONCLUDING REMARKS 150
REFERENCES 151
5 RECENT PROGRESS IN FLUCTUATION THEOREMS AND FREE ENERGY RECOVERY 155
ANNA ALEMANY, MARCO RIBEZZI-CRIVELLARI, AND FELIX RITORT 5.1
INTRODUCTION 155
5.2 FREE ENERGY MEASUREMENT PRIOR TO FLUCTUATION THEOREMS 156 5.2.1
EXPERIMENTAL METHODS FOR FE MEASUREMENTS 156 5.2.2 COMPUTATIONAL FE
ESTIMATES 158
5.3 SINGLE-MOLECULE EXPERIMENTS 159
5.3.1 EXPERIMENTAL TECHNIQUES 160
5.3.2 PULLING DNA HAIRPINS WITH OPTICAL TWEEZERS 162 5.4 FLUCTUATION
RELATIONS 163
5.4.1 EXPERIMENTAL VALIDATION O F THE CROOKS EQUALITY 165 5.5 CONTROL
PARAMETERS, CONFIGURATIONAL VARIABLES, AND T H E DEFINITION O F WORK 166
5.5.1 ABOUT THE RIGHT DEFINITION O F WORK: ACCUMULATED VERSUS
TRANSFERRED WORK 168 5.6 EXTENDED FLUCTUATION RELATIONS 172
5.6.1 EXPERIMENTAL MEASUREMENT O F THE POTENTIAL O F MEAN FORCE 174 5.7
FREE ENERGY RECOVERY FROM UNIDIRECTIONAL WORK MEASUREMENTS 175 5.8
CONCLUSIONS 177
REFERENCES 177
IMAGE 4
V I I I CONTENTS
6 INFORMATION THERMODYNAMICS: MAXWELL'S DEMON IN NONEQUILIBRIUM
DYNAMICS 181 TAKAHIRO SAGAWA AND MASAHITO UEDA 6.1 INTRODUCTION 181
6.2 SZILARD ENGINE 182
6.3 INFORMATION CONTENT I N THERMODYNAMICS 184
6.3.1 SHANNON INFORMATION 184
6.3.2 MUTUAL INFORMATION 185
6.3.3 EXAMPLES 187
6.4 SECOND LAW O F THERMODYNAMICS WITH FEEDBACK CONTROL 189 6.4.1
GENERAL BOUND 190
6.4.2 GENERALIZED SZILARD ENGINE 191
6.4.3 OVERDAMPED LANGEVIN SYSTEM 192 6.4.4 EXPERIMENTAL DEMONSTRATION:
FEEDBACK-CONTROLLED RATCHET 194 6.4.5 CARNOT EFFICIENCY WITH TWO HEAT
BATHS 196 6.5 NONEQUILIBRIUM EQUALITIES WITH FEEDBACK CONTROL 197 6.5.1
PRELIMINARIES 197
6.5.2 MEASUREMENT AND FEEDBACK 200
6.5.3 NONEQUILIBRIUM EQUALITIES WITH MUTUAL INFORMATION 201 6.5.4
NONEQUILIBRIUM EQUALITIES WITH EFFICACY PARAMETER 203 6.6 THERMODYNAMIC
ENERGY COST FOR MEASUREMENT AND INFORMATION ERASURE 205
6.7 CONCLUSIONS 208
APPENDIX 6. A: PROOF O F EQ. (6.56) 208 REFERENCES 209
7 TIME-REVERSAL SYMMETRY RELATIONS FOR CURRENTS IN QUANTUM AND
STOCHASTIC NONEQUILIBRIUM SYSTEMS 213 PIERRE CASPARD 7.1 INTRODUCTION
213
7.2 FUNCTIONAL SYMMETRY RELATIONS AND RESPONSE THEORY 216 7.3 TRANSITORY
CURRENT FLUCTUATION THEOREM 220
7.4 FROM TRANSITORY TO THE STATIONARY CURRENT FLUCTUATION THEOREM 224
7.5 CURRENT FLUCTUATION THEOREM A N D RESPONSE THEORY 227 7.6 CASE O F
INDEPENDENT PARTICLES 230
7.7 TIME-REVERSAL SYMMETRY RELATIONS I N THE MASTER EQUATION APPROACH
238 7.7.1 CURRENT FLUCTUATION THEOREM FOR STOCHASTIC PROCESSES 238 1.1.2
THERMODYNAMIC ENTROPY PRODUCTION 241
7.7.3 CASE O F EFFUSION PROCESSES 241
7.7 .4 STATISTICS O F HISTORIES AND TIME REVERSAL 242 7.8 TRANSPORT I N
ELECTRONIC CIRCUITS 244
7.8.1 Q U A N T U M DOT WITH ONE RESONANT LEVEL 244 7.8.2 CAPACITIVELY
COUPLED CIRCUITS 245 7.8.3 COHERENT Q U A N T U M CONDUCTOR 250
IMAGE 5
CONTENTS I X
7.9 CONCLUSIONS 252
REFERENCES 254
8 ANOMALOUS FLUCTUATION RELATIONS 259
RAINER KLAGES, ALEKSEI V. CHECHKIN, AND PETER DIETERICH 8.1 INTRODUCTION
259
8.2 TRANSIENT FLUCTUATION RELATIONS 260
8.2.1 MOTIVATION 260
8.2.2 SCALING 262
8.2.3 TRANSIENT FLUCTUATION RELATION FOR ORDINARY LANGEVIN DYNAMICS 263
8.3 TRANSIENT WORK FLUCTUATION RELATIONS FOR ANOMALOUS DYNAMICS 265
8.3.1 GAUSSIAN STOCHASTIC PROCESSES 265
8.3.1.1 CORRELATED INTERNAL GAUSSIAN NOISE 265 8.3.1.2 CORRELATED
EXTERNAL GAUSSIAN NOISE 266 8.3.2 LEVY FLIGHTS 267
8.3.3 TIME-FRACTIONAL KINETICS 268
8.4 ANOMALOUS DYNAMICS O F BIOLOGICAL CELL MIGRATION 269 8.4.1 CELL
MIGRATION I N EQUILIBRIUM 270
8.4.1.1 EXPERIMENTAL RESULTS 271 8.4.1.2 THEORETICAL MODELING 272 8.4.2
CELL MIGRATION UNDER CHEMICAL GRADIENTS 275 8.5 CONCLUSIONS 277
REFERENCES 278
PART II BEYOND FLUCTUATION RELATIONS 283
9 OUT-OF-EQUILIBRIUM GENERALIZED FLUCTUATION-DISSIPATION RELATIONS 285
G. CRADENIGO, A. PUGLISI, A. SARRACINO, D. VILLAMAINA, AND A. VULPIANI
9.1 INTRODUCTION 285
9.1.1 THE RELEVANCE O F FLUCTUATIONS: FEW HISTORICAL COMMENTS 286 9.2
GENERALIZED FLUCTUATION-DISSIPATION RELATIONS 287 9.2.1 CHAOS AND THE
FDR: VAN KAMPEN'S OBJECTION 287 9.2.2 GENERALIZED FDR FOR STATIONARY
SYSTEMS 288
9.2.3 REMARKS ON THE INVARIANT MEASURE 290
9.2.4 GENERALIZED FDR FOR MARKOVIAN SYSTEMS 292 9.3 RANDOM WALK O N A
COMB LATTICE 294
9.3.1 ANOMALOUS DIFFUSION AND FDR 294
9.3.2 TRANSITION RATES O F THE MODEL 295
9.3.3 ANOMALOUS DYNAMICS 296
9.3.4 APPLICATION O F THE GENERALIZED FDR 297 9.4 ENTROPY PRODUCTION 300
9.5 LANGEVIN PROCESSES WITHOUT DETAILED BALANCE 301 9.5.1 MARKOVIAN
LINEAR SYSTEM 302
9.5.2 FLUCTUATION-RESPONSE RELATION 303
IMAGE 6
X CONTENTS
9.5.3 ENTROPY PRODUCTION 305
9.6 GRANULAR INTRUDER 306
9.6.1 MODEL 3 0 7
9.6.2 DENSE CASE: DOUBLE LANGEVIN WITH TWO TEMPERATURES 309 9.6.3
GENERALIZED FDR AND ENTROPY PRODUCTION 311 9.7 CONCLUSIONS A N D
PERSPECTIVES 313
REFERENCES 314
10 ANOMALOUS THERMAL TRANSPORT IN NANOSTRUCTURES 319 GANG ZHANG, SHA
LIU, AND BAOWEN LI 10.1 INTRODUCTION 319
10.2 NUMERICAL STUDY O N THERMAL CONDUCTIVITY AND HEAT ENERGY DIFFUSION
IN ONE-DIMENSIONAL SYSTEMS 320 10.3 BREAKDOWN O F FOURIER'S LAW.
EXPERIMENTAL EVIDENCE 325 10.4 THEORETICAL MODELS 327
10.5 CONCLUSIONS 331
REFERENCES 332
11 LARGE DEVIATION APPROACH TO NONEQUILIBRIUM SYSTEMS 335 HUGO TOUCHETTE
AND ROSEMARY J. HARRIS 11.1 INTRODUCTION 335
11.2 FROM EQUILIBRIUM TO NONEQUILIBRIUM SYSTEMS 336 11.2.1 EQUILIBRIUM
SYSTEMS 336
11.2.2 NONEQUILIBRIUM SYSTEMS 339 11.2.3 EQUILIBRIUM VERSUS
NONEQUILIBRIUM SYSTEMS 340 11.3 ELEMENTS O F LARGE DEVIATION THEORY 341
11.3.1 GENERAL RESULTS 341
11.3.2 EQUILIBRIUM LARGE DEVIATIONS 343 11.3.3 NONEQUILIBRIUM LARGE
DEVIATIONS 345 11.4 APPLICATIONS TO NONEQUILIBRIUM SYSTEMS 347 11.4.1
RANDOM WALKERS I N DISCRETE A N D CONTINUOUS TIME 347
11.4.2 LARGE DEVIATION PRINCIPLE FOR DENSITY PROFILES 349 11.4.3 LARGE
DEVIATION PRINCIPLE FOR CURRENT FLUCTUATIONS 350 11.4.4 INTERACTING
PARTICLE SYSTEMS: FEATURES AND SUBTLETIES 352
11.4.5 MACROSCOPIC FLUCTUATION THEORY 354 11.5 FINAL REMARKS 356
REFERENCES 357
12 LYAPUNOV MODES IN EXTENDED SYSTEMS 361
HONG-LIU YANG AND CUNTER RADONS 12.1 INTRODUCTION 361
12.2 NUMERICAL ALGORITHMS A N D LV CORRELATIONS 363 12.3 UNIVERSALITY
CLASSES O F HYDRODYNAMIC LYAPUNOV MODES 365 12.4 HYPERBOLICITY AND THE
SIGNIFICANCE O F LYAPUNOV MODES 369
IMAGE 7
CONTENTS | X I
12.5 LYAPUNOV SPECTRAL GAP A N D BRANCH SPLITTING O F LYAPUNOV MODES I N
A
"DIATOMIC" SYSTEM 372 12.6 COMPARISON O F COVARIANT AND ORTHOGONAL HLMS
376 12.7 HYPERBOLICITY AND EFFECTIVE DEGREES O F FREEDOM O F PARTIAL
DIFFERENTIAL EQUATIONS 380 12.8 PROBING THE LOCAL GEOMETRIC STRUCTURE O
F INERTIAL MANIFOLDS VIA A
PROJECTION METHOD 384 12.9 SUMMARY 388
REFERENCES 389
13 STUDY O F SINGLE-MOLECULE DYNAMICS IN MESOPOROUS SYSTEMS, CLASSES,
AND LIVING CELLS 393 STEPHAN MACKOWIAK AND CHRISTOPH BRAUCHLE
13.1 INTRODUCTION 393
13.1.1 EXPERIMENTAL METHOD 393
13.1.2 ANALYSIS O F THE SINGLE-MOLECULE TRAJECTORIES 395 13.2
INVESTIGATION O F THE STRUCTURE O F MESOPOROUS SILICA EMPLOYING
SINGLEMOLECULE MICROSCOPY 396
13.2.1 MESOPOROUS SILICA 396
13.2.2 COMBINING TEM A N D SMM FOR STRUCTURE DETERMINATION O F
MESOPOROUS SILICA 398
13.2.3 APPLICATIONS O F SMM TO IMPROVE THE SYNTHESIS O F MESOPOROUS
SYSTEMS 399 13.3 INVESTIGATION O F THE DIFFUSION O F GUEST MOLECULES I N
MESOPOROUS SYSTEMS 402 13.3.1 A MORE DETAILED LOOK INTO THE DIFFUSIONAL
DYNAMICS O F GUEST
MOLECULES IN NANOPORES 402 13.3.2 MODIFICATION O F THE FLOW MEDIUM IN
THE NANOPORES AND ITS INFLUENCE O N PROBE DIFFUSION 404 13.3.3 LOADING O
F CARGOES INTO MESOPORES: A STEP TOWARD DRUG DELIVERY
APPLICATIONS 406
13.4 A TEST O F THE ERGODIC THEOREM BY EMPLOYING SINGLE-MOLECULE
MICROSCOPY 407 13.5 SINGLE-PARTICLE TRACKING IN BIOLOGICAL SYSTEMS 409
13.6 CONCLUSION A N D OUTLOOK 412
REFERENCES 413
INDEX 415 |
| any_adam_object | 1 |
| author2 | Klages, Rainer 1966- |
| author2_role | edt |
| author2_variant | r k rk |
| author_GND | (DE-588)114197547 |
| author_facet | Klages, Rainer 1966- |
| building | Verbundindex |
| bvnumber | BV040797512 |
| classification_rvk | UG 2000 UG 3100 UG 3500 |
| ctrlnum | (OCoLC)835334647 (DE-599)DNB1025272048 |
| dewey-full | 530 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 530.13 |
| dewey-search | 530 530.13 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV040797512 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:36:03Z |
| institution | BVB |
| isbn | 9783527410941 9783527658701 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025777681 |
| oclc_num | 835334647 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM DE-83 DE-703 DE-29T DE-355 DE-BY-UBR |
| owner_facet | DE-11 DE-19 DE-BY-UBM DE-83 DE-703 DE-29T DE-355 DE-BY-UBR |
| physical | XXVIII, 418 S. Ill., graph. Darst. 240 mm x 170 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Wiley-VCH |
| record_format | marc |
| series2 | Reviews of Nonlinear Dynamics and Complexity |
| spelling | Nonequilibrium statistical physics of small systems fluctuation relations and beyond ed. by Rainer Klages ... Weinheim Wiley-VCH 2013 XXVIII, 418 S. Ill., graph. Darst. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier Reviews of Nonlinear Dynamics and Complexity Physikalisches System (DE-588)4174610-7 gnd rswk-swf Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf Kleines System (DE-588)4164125-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Physikalisches System (DE-588)4174610-7 s Kleines System (DE-588)4164125-5 s Nichtgleichgewichtsstatistik (DE-588)4136220-2 s DE-604 Klages, Rainer 1966- (DE-588)114197547 edt Erscheint auch als Online-Ausgabe, EPUB 978-3-527-65872-5 Erscheint auch als Online-Ausgabe, MOBI 978-3-527-65871-8 Erscheint auch als Online-Ausgabe, PDF 978-3-527-65873-2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4102909&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025777681&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nonequilibrium statistical physics of small systems fluctuation relations and beyond Physikalisches System (DE-588)4174610-7 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Kleines System (DE-588)4164125-5 gnd |
| subject_GND | (DE-588)4174610-7 (DE-588)4136220-2 (DE-588)4164125-5 (DE-588)4143413-4 |
| title | Nonequilibrium statistical physics of small systems fluctuation relations and beyond |
| title_auth | Nonequilibrium statistical physics of small systems fluctuation relations and beyond |
| title_exact_search | Nonequilibrium statistical physics of small systems fluctuation relations and beyond |
| title_full | Nonequilibrium statistical physics of small systems fluctuation relations and beyond ed. by Rainer Klages ... |
| title_fullStr | Nonequilibrium statistical physics of small systems fluctuation relations and beyond ed. by Rainer Klages ... |
| title_full_unstemmed | Nonequilibrium statistical physics of small systems fluctuation relations and beyond ed. by Rainer Klages ... |
| title_short | Nonequilibrium statistical physics of small systems |
| title_sort | nonequilibrium statistical physics of small systems fluctuation relations and beyond |
| title_sub | fluctuation relations and beyond |
| topic | Physikalisches System (DE-588)4174610-7 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Kleines System (DE-588)4164125-5 gnd |
| topic_facet | Physikalisches System Nichtgleichgewichtsstatistik Kleines System Aufsatzsammlung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4102909&prov=M&dok%5Fvar=1&dok%5Fext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025777681&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT klagesrainer nonequilibriumstatisticalphysicsofsmallsystemsfluctuationrelationsandbeyond |