Statistical physics: an introduction
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2007
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| Item Description: | Angekündigt u.d.T.: Yoshioka, Daijiro: Introduction to statistical physics |
| Physical Description: | XII, 208 S. Ill., graph. Darst. |
| ISBN: | 3540286055 9783540286059 |
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| 020 | |a 9783540286059 |9 978-3-540-28605-9 | ||
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| 100 | 1 | |a Yoshioka, Daijiro |d 1949- |e Verfasser |0 (DE-588)123454190 |4 aut | |
| 245 | 1 | 0 | |a Statistical physics |b an introduction |c Daijiro Yoshioka |
| 246 | 1 | 3 | |a Introduction to statistical physics |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XII, 208 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Angekündigt u.d.T.: Yoshioka, Daijiro: Introduction to statistical physics | ||
| 650 | 4 | |a Physique statistique | |
| 650 | 4 | |a Statistical physics | |
| 650 | 0 | 7 | |a Statistische Physik |0 (DE-588)4057000-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Statistische Physik |0 (DE-588)4057000-9 |D s |
| 689 | 0 | |5 DE-604 | |
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| adam_text | CONTENTS
PART
I
GENERAL
PRINCIPLES
1
THERMAL
EQUILIBRIUM
AND
THE
PRINCIPLE
OF
EQUAL
PROBABILITY
.......................................
3
1.1
INTRODUCTIONTOTHERMALANDSTATISTICALPHYSICS.............
3
1.2
THERMAL
EQUILIBRIUM
....................................
4
1.2.1
DESCRIPTION
OF
A
SYSTEM
IN
EQUILIBRIUM...............
4
1.2.2
STATEVARIABLES,WORK,ANDHEAT
....................
5
1.2.3
TEMPERATURE
AND
THE
ZEROTH
LAW
OF
THERMODYNAMICS..
7
1.2.4
HEATCAPACITYANDSPECIFICHEAT
....................
8
1.3
KINETICTHEORYOFGASMOLECULES
..........................
9
1.3.1
THESPATIALDISTRIBUTIONOFGASMOLECULES............
10
1.3.2
VELOCITYDISTRIBUTIONOFANIDEALGAS
................
15
1.3.3
THEPRESSUREOFAGAS
.............................
18
1.4
THE
PRINCIPLE
OF
EQUAL
PROBABILITY.........................
20
2
ENTROPY
...................................................
23
2.1
THEMICROCANONICALDISTRIBUTION
..........................
23
2.2
NUMBEROFSTATESANDDENSITYOFSTATES
....................
26
2.3
CONDITIONS
FOR
THERMAL
EQUILIBRIUM
.......................
28
2.3.1
EQUILIBRIUM
CONDITION
WHENONLYENERGYISEXCHANGED.....................
28
2.3.2
EQUILIBRIUM
CONDITION
WHEN
MOLECULES
ARE
EXCHANGED
.
30
2.3.3
EQUILIBRIUM
CONDITION
WHEN
TWO
SYSTEMS
SHAREACOMMONVOLUME...........................
31
2.4
THERMAL
NONEQUILIBRIUM
AND
IRREVERSIBLE
PROCESSES
..........
32
3
THE
PARTITION
FUNCTION
AND
THE
FREE
ENERGY
...............
35
3.1
ASYSTEMINAHEATBATH.................................
35
3.1.1
CANONICALDISTRIBUTION.............................
36
3.1.2
APPLICATIONTOAMOLECULEINGAS....................
37
VIII
CONTENTS
3.2
PARTITIONFUNCTION.......................................
38
3.3
FREEENERGY
............................................
39
3.4
INTERNALENERGY
.........................................
41
3.5
THERMODYNAMIC
FUNCTIONS
ANDLEGENDRETRANSFORMATIONS
............................
42
3.6
MAXWELLRELATIONS.......................................
43
PART
II
ELEMENTARY
APPLICATIONS
4
IDEAL
GASES
................................................
47
4.1
QUANTUMMECHANICSOFAGASMOLECULE.....................
47
4.2
PHASESPACEANDTHENUMBEROFMICROSCOPICSTATES..........
49
4.3
ENTROPYOFANIDEALGAS..................................
51
4.4
PRESSURE
OF
AN
IDEAL
GAS:
QUANTUMMECHANICALTREATMENT
..........................
54
4.5
STATISTICAL-MECHANICALTEMPERATUREANDPRESSURE............
55
4.6
PARTITIONFUNCTIONOFANIDEALGAS.........................
56
4.7
DIATOMICMOLECULES......................................
58
4.7.1
DECOMPOSITIONOFTHEPARTITIONFUNCTION
.............
58
4.7.2
CENTER-OF-GRAVITY
PART:
Z
(CG)
......................
60
4.7.3
VIBRATIONAL
PART:
Z
(V)
.............................
61
4.7.4
ROTATIONAL
PART:
Z
(R)
..............................
64
5
THE
HEAT
CAPACITY
OF
A
SOLID,
AND
BLACK-BODY
RADIATION
.................................
67
5.1
HEATCAPACITYOFASOLIDI-EINSTEINMODEL
................
67
5.2
HEATCAPACITYOFASOLIDII-DEBYEMODEL
.................
70
5.2.1
COLLECTIVE
OSCILLATIONS
OF
THE
LATTICE
ANDTHEINTERNALENERGY............................
70
5.2.2
HEATCAPACITYATHIGHTEMPERATURE
.................
73
5.2.3
HEATCAPACITYATLOWTEMPERATURE..................
74
5.2.4
HEATCAPACITYATINTERMEDIATETEMPERATURE
..........
74
5.2.5
PHYSICAL
EXPLANATION
FOR
THE
TEMPERATURE
DEPENDENCE.
75
5.3
BLACK-BODYRADIATION....................................
76
5.3.1
WIEN SLAWANDSTEFAN SLAW.......................
76
5.3.2
ENERGYOFRADIATIONINACAVITY.....................
77
5.3.3
SPECTRUMOFLIGHTEMITTEDFROMAHOLE
..............
78
5.3.4
THETEMPERATUREOFTHEUNIVERSE....................
80
6
THE
ELASTICITY
OF
RUBBER
..................................
83
6.1
CHARACTERISTICSOFRUBBER
................................
83
6.2
MODELOFRUBBER........................................
84
6.3
ENTROPYOFRUBBER
......................................
85
6.4
HOOKE SLAW............................................
86
CONTENTS
IX
7
MAGNETIC
MATERIALS
........................................
89
7.1
ORIGINOFPERMANENTMAGNETISM...........................
89
7.2
STATISTICALMECHANICSOFAFREESPINSYSTEM.................
91
7.2.1
MODELANDENTROPY................................
91
7.2.2
FREE
ENERGY,
MAGNETIZATION,
AND
SUSCEPTIBILITY
........
93
7.2.3
INTERNALENERGYANDHEATCAPACITY..................
95
7.3
ISINGMODEL-MEAN-FIELDAPPROXIMATION...................
97
7.3.1
LINKS
............................................
97
7.3.2
MEAN-FIELDAPPROXIMATION
.........................
99
7.3.3
SOLUTIONOFTHESELF-CONSISTENTEQUATION..............100
7.3.4
ENTROPYANDHEATCAPACITY.........................103
7.3.5
SUSCEPTIBILITY
.....................................105
7.3.6
DOMAINSTRUCTURE
.................................106
7.4
THEONE-DIMENSIONALISINGMODEL.........................106
7.4.1
FREEENERGY
......................................106
7.4.2
ENTROPYANDHEATCAPACITY.........................108
7.4.3
MAGNETIZATION
AND
SUSCEPTIBILITY
....................110
PART
III
MORE
ADVANCED
TOPICS
8
FIRST-ORDER
PHASE
TRANSITIONS
.............................
115
8.1
THEVARIOUSPHASESOFMATTER.............................115
8.2
SYSTEM
IN
A
HEAT
BATH
AT
FIXED
P
AND
T
...................119
8.3
COEXISTENCEOFPHASES....................................121
8.4
THECLAUSIUS-CLAPEYRONLAW
.............................123
8.5
THECRITICALPOINT.......................................126
8.6
THEVANDERWAALSGAS
..................................128
8.6.1
COEXISTENCEOFGASANDLIQUID......................130
9
SECOND-ORDER
PHASE
TRANSITIONS
...........................
133
9.1
VARIOUSPHASETRANSITIONSANDORDERPARAMETERS............133
9.2
LANDAUTHEORY
.........................................134
9.2.1
FREEENERGY
......................................137
9.2.2
ENTROPY,INTERNALENERGY,ANDHEATCAPACITY
.........138
9.2.3
CRITICALPHENOMENA................................139
9.3
THETWO-DIMENSIONALISINGMODEL.........................140
10
DENSE
GASES
-
IDEAL
GASES
AT
LOW
TEMPERATURE
...........
147
10.1
THE
PHASE
SPACE
FOR
N
IDENTICALPARTICLES..................147
10.2
THEGRANDCANONICALDISTRIBUTION.........................149
10.3
IDEALFERMIGASESANDIDEALBOSEGASES....................151
10.3.1
OCCUPATIONNUMBERREPRESENTATION
.................151
10.3.2
THERMODYNAMICFUNCTIONS
.........................154
XC
O
N
T
E
N
T
S
10.4
PROPERTIESOFAFREE-FERMIONGAS..........................154
10.4.1
PROPERTIES
AT
T
=0................................157
10.4.2
PROPERTIESATLOWTEMPERATURE
.....................160
10.5
PROPERTIESOFAFREE-BOSONGAS............................169
10.5.1
THETWOKINDSOFBOSEGAS
........................169
10.5.2
PROPERTIESATLOWTEMPERATURE
.....................170
10.6
PROPERTIESOFGASESATHIGHTEMPERATURE...................178
PART
IV
APPENDICES
A
FORMULAS
RELATED
TO
THE
FACTORIAL
FUNCTION
................
185
A.1
BINOMIALCOEFFICIENTSANDBINOMIALTHEOREM................185
A.2
STIRLING SFORMULA
.......................................185
A.3
N
!!.....................................................186
B
THE
GAUSSIAN
DISTRIBUTION
FUNCTION
.......................
187
B.1
THECENTRALLIMITTHEOREM
..............................187
B.1.1
EXAMPLE
.........................................188
B.2
GAUSSIANINTEGRALS.......................................188
B.3
THE
FOURIER
TRANSFORM
OF
A
GAUSSIAN
DISTRIBUTION
FUNCTION...189
C
LAGRANGE S
METHOD
OF
UNDETERMINED
MULTIPLIERS
...............................
191
C.1
EXAMPLE
...............................................192
C.2
GENERALIZATION
..........................................192
D
VOLUME
OF
A
HYPERSPHERE
..................................
193
E
HYPERBOLIC
FUNCTIONS
......................................
195
F
BOUNDARY
CONDITIONS
......................................
197
F.1
FIXED
BOUNDARY
CONDITION
...............................197
F.2
PERIODIC
BOUNDARY
CONDITION
.............................198
G
THE
RIEMANN
ZETA
FUNCTION
...............................
201
REFERENCES
.....................................................
203
INDEX
..........................................................
205
|
| adam_txt |
CONTENTS
PART
I
GENERAL
PRINCIPLES
1
THERMAL
EQUILIBRIUM
AND
THE
PRINCIPLE
OF
EQUAL
PROBABILITY
.
3
1.1
INTRODUCTIONTOTHERMALANDSTATISTICALPHYSICS.
3
1.2
THERMAL
EQUILIBRIUM
.
4
1.2.1
DESCRIPTION
OF
A
SYSTEM
IN
EQUILIBRIUM.
4
1.2.2
STATEVARIABLES,WORK,ANDHEAT
.
5
1.2.3
TEMPERATURE
AND
THE
ZEROTH
LAW
OF
THERMODYNAMICS.
7
1.2.4
HEATCAPACITYANDSPECIFICHEAT
.
8
1.3
KINETICTHEORYOFGASMOLECULES
.
9
1.3.1
THESPATIALDISTRIBUTIONOFGASMOLECULES.
10
1.3.2
VELOCITYDISTRIBUTIONOFANIDEALGAS
.
15
1.3.3
THEPRESSUREOFAGAS
.
18
1.4
THE
PRINCIPLE
OF
EQUAL
PROBABILITY.
20
2
ENTROPY
.
23
2.1
THEMICROCANONICALDISTRIBUTION
.
23
2.2
NUMBEROFSTATESANDDENSITYOFSTATES
.
26
2.3
CONDITIONS
FOR
THERMAL
EQUILIBRIUM
.
28
2.3.1
EQUILIBRIUM
CONDITION
WHENONLYENERGYISEXCHANGED.
28
2.3.2
EQUILIBRIUM
CONDITION
WHEN
MOLECULES
ARE
EXCHANGED
.
30
2.3.3
EQUILIBRIUM
CONDITION
WHEN
TWO
SYSTEMS
SHAREACOMMONVOLUME.
31
2.4
THERMAL
NONEQUILIBRIUM
AND
IRREVERSIBLE
PROCESSES
.
32
3
THE
PARTITION
FUNCTION
AND
THE
FREE
ENERGY
.
35
3.1
ASYSTEMINAHEATBATH.
35
3.1.1
CANONICALDISTRIBUTION.
36
3.1.2
APPLICATIONTOAMOLECULEINGAS.
37
VIII
CONTENTS
3.2
PARTITIONFUNCTION.
38
3.3
FREEENERGY
.
39
3.4
INTERNALENERGY
.
41
3.5
THERMODYNAMIC
FUNCTIONS
ANDLEGENDRETRANSFORMATIONS
.
42
3.6
MAXWELLRELATIONS.
43
PART
II
ELEMENTARY
APPLICATIONS
4
IDEAL
GASES
.
47
4.1
QUANTUMMECHANICSOFAGASMOLECULE.
47
4.2
PHASESPACEANDTHENUMBEROFMICROSCOPICSTATES.
49
4.3
ENTROPYOFANIDEALGAS.
51
4.4
PRESSURE
OF
AN
IDEAL
GAS:
QUANTUMMECHANICALTREATMENT
.
54
4.5
STATISTICAL-MECHANICALTEMPERATUREANDPRESSURE.
55
4.6
PARTITIONFUNCTIONOFANIDEALGAS.
56
4.7
DIATOMICMOLECULES.
58
4.7.1
DECOMPOSITIONOFTHEPARTITIONFUNCTION
.
58
4.7.2
CENTER-OF-GRAVITY
PART:
Z
(CG)
.
60
4.7.3
VIBRATIONAL
PART:
Z
(V)
.
61
4.7.4
ROTATIONAL
PART:
Z
(R)
.
64
5
THE
HEAT
CAPACITY
OF
A
SOLID,
AND
BLACK-BODY
RADIATION
.
67
5.1
HEATCAPACITYOFASOLIDI-EINSTEINMODEL
.
67
5.2
HEATCAPACITYOFASOLIDII-DEBYEMODEL
.
70
5.2.1
COLLECTIVE
OSCILLATIONS
OF
THE
LATTICE
ANDTHEINTERNALENERGY.
70
5.2.2
HEATCAPACITYATHIGHTEMPERATURE
.
73
5.2.3
HEATCAPACITYATLOWTEMPERATURE.
74
5.2.4
HEATCAPACITYATINTERMEDIATETEMPERATURE
.
74
5.2.5
PHYSICAL
EXPLANATION
FOR
THE
TEMPERATURE
DEPENDENCE.
75
5.3
BLACK-BODYRADIATION.
76
5.3.1
WIEN'SLAWANDSTEFAN'SLAW.
76
5.3.2
ENERGYOFRADIATIONINACAVITY.
77
5.3.3
SPECTRUMOFLIGHTEMITTEDFROMAHOLE
.
78
5.3.4
THETEMPERATUREOFTHEUNIVERSE.
80
6
THE
ELASTICITY
OF
RUBBER
.
83
6.1
CHARACTERISTICSOFRUBBER
.
83
6.2
MODELOFRUBBER.
84
6.3
ENTROPYOFRUBBER
.
85
6.4
HOOKE'SLAW.
86
CONTENTS
IX
7
MAGNETIC
MATERIALS
.
89
7.1
ORIGINOFPERMANENTMAGNETISM.
89
7.2
STATISTICALMECHANICSOFAFREESPINSYSTEM.
91
7.2.1
MODELANDENTROPY.
91
7.2.2
FREE
ENERGY,
MAGNETIZATION,
AND
SUSCEPTIBILITY
.
93
7.2.3
INTERNALENERGYANDHEATCAPACITY.
95
7.3
ISINGMODEL-MEAN-FIELDAPPROXIMATION.
97
7.3.1
LINKS
.
97
7.3.2
MEAN-FIELDAPPROXIMATION
.
99
7.3.3
SOLUTIONOFTHESELF-CONSISTENTEQUATION.100
7.3.4
ENTROPYANDHEATCAPACITY.103
7.3.5
SUSCEPTIBILITY
.105
7.3.6
DOMAINSTRUCTURE
.106
7.4
THEONE-DIMENSIONALISINGMODEL.106
7.4.1
FREEENERGY
.106
7.4.2
ENTROPYANDHEATCAPACITY.108
7.4.3
MAGNETIZATION
AND
SUSCEPTIBILITY
.110
PART
III
MORE
ADVANCED
TOPICS
8
FIRST-ORDER
PHASE
TRANSITIONS
.
115
8.1
THEVARIOUSPHASESOFMATTER.115
8.2
SYSTEM
IN
A
HEAT
BATH
AT
FIXED
P
AND
T
.119
8.3
COEXISTENCEOFPHASES.121
8.4
THECLAUSIUS-CLAPEYRONLAW
.123
8.5
THECRITICALPOINT.126
8.6
THEVANDERWAALSGAS
.128
8.6.1
COEXISTENCEOFGASANDLIQUID.130
9
SECOND-ORDER
PHASE
TRANSITIONS
.
133
9.1
VARIOUSPHASETRANSITIONSANDORDERPARAMETERS.133
9.2
LANDAUTHEORY
.134
9.2.1
FREEENERGY
.137
9.2.2
ENTROPY,INTERNALENERGY,ANDHEATCAPACITY
.138
9.2.3
CRITICALPHENOMENA.139
9.3
THETWO-DIMENSIONALISINGMODEL.140
10
DENSE
GASES
-
IDEAL
GASES
AT
LOW
TEMPERATURE
.
147
10.1
THE
PHASE
SPACE
FOR
N
IDENTICALPARTICLES.147
10.2
THEGRANDCANONICALDISTRIBUTION.149
10.3
IDEALFERMIGASESANDIDEALBOSEGASES.151
10.3.1
OCCUPATIONNUMBERREPRESENTATION
.151
10.3.2
THERMODYNAMICFUNCTIONS
.154
XC
O
N
T
E
N
T
S
10.4
PROPERTIESOFAFREE-FERMIONGAS.154
10.4.1
PROPERTIES
AT
T
=0.157
10.4.2
PROPERTIESATLOWTEMPERATURE
.160
10.5
PROPERTIESOFAFREE-BOSONGAS.169
10.5.1
THETWOKINDSOFBOSEGAS
.169
10.5.2
PROPERTIESATLOWTEMPERATURE
.170
10.6
PROPERTIESOFGASESATHIGHTEMPERATURE.178
PART
IV
APPENDICES
A
FORMULAS
RELATED
TO
THE
FACTORIAL
FUNCTION
.
185
A.1
BINOMIALCOEFFICIENTSANDBINOMIALTHEOREM.185
A.2
STIRLING'SFORMULA
.185
A.3
N
!!.186
B
THE
GAUSSIAN
DISTRIBUTION
FUNCTION
.
187
B.1
THECENTRALLIMITTHEOREM
.187
B.1.1
EXAMPLE
.188
B.2
GAUSSIANINTEGRALS.188
B.3
THE
FOURIER
TRANSFORM
OF
A
GAUSSIAN
DISTRIBUTION
FUNCTION.189
C
LAGRANGE'S
METHOD
OF
UNDETERMINED
MULTIPLIERS
.
191
C.1
EXAMPLE
.192
C.2
GENERALIZATION
.192
D
VOLUME
OF
A
HYPERSPHERE
.
193
E
HYPERBOLIC
FUNCTIONS
.
195
F
BOUNDARY
CONDITIONS
.
197
F.1
FIXED
BOUNDARY
CONDITION
.197
F.2
PERIODIC
BOUNDARY
CONDITION
.198
G
THE
RIEMANN
ZETA
FUNCTION
.
201
REFERENCES
.
203
INDEX
.
205 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Yoshioka, Daijiro 1949- |
| author_GND | (DE-588)123454190 |
| author_facet | Yoshioka, Daijiro 1949- |
| author_role | aut |
| author_sort | Yoshioka, Daijiro 1949- |
| author_variant | d y dy |
| building | Verbundindex |
| bvnumber | BV021658186 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.8 |
| callnumber-search | QC174.8 |
| callnumber-sort | QC 3174.8 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 3500 |
| ctrlnum | (OCoLC)79584297 (DE-599)BVBBV021658186 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV021658186 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:05:07Z |
| indexdate | 2024-07-09T20:40:59Z |
| institution | BVB |
| isbn | 3540286055 9783540286059 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014872717 |
| oclc_num | 79584297 |
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| physical | XII, 208 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Yoshioka, Daijiro 1949- Verfasser (DE-588)123454190 aut Statistical physics an introduction Daijiro Yoshioka Introduction to statistical physics Berlin [u.a.] Springer 2007 XII, 208 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Angekündigt u.d.T.: Yoshioka, Daijiro: Introduction to statistical physics Physique statistique Statistical physics Statistische Physik (DE-588)4057000-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Physik (DE-588)4057000-9 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2669189&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014872717&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yoshioka, Daijiro 1949- Statistical physics an introduction Physique statistique Statistical physics Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Statistical physics an introduction |
| title_alt | Introduction to statistical physics |
| title_auth | Statistical physics an introduction |
| title_exact_search | Statistical physics an introduction |
| title_exact_search_txtP | Statistical physics an introduction |
| title_full | Statistical physics an introduction Daijiro Yoshioka |
| title_fullStr | Statistical physics an introduction Daijiro Yoshioka |
| title_full_unstemmed | Statistical physics an introduction Daijiro Yoshioka |
| title_short | Statistical physics |
| title_sort | statistical physics an introduction |
| title_sub | an introduction |
| topic | Physique statistique Statistical physics Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Physique statistique Statistical physics Statistische Physik Lehrbuch |
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