Ruelle D. — Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics :: Электронная библиотека попечительского совета мехмата МГУ

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Ruelle D. — Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics

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Название: Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics

Автор: Ruelle D.

Аннотация:

Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2004

Количество страниц: 174

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Algebra at infinity      19
Anosov diffeomorphism      143
Anosov’s closing lemma      124
Axiom      see “Condition”
Axiom A diffeomorphism      143
Basic set      124
Bernoulli flow      163
Bernoulli shift      79 128 155
Borel set      154
Boundary term      16
Cluster property      19 21 40
Cluster property, exponential      96
Cohomological interpretation      161
Commuting continuous maps      112
Condition, (+T), (+T'), (+T'')      148
Condition, (A), (B), (C)      20
Condition, (A’), (B’), (C)      21
Condition, (D)      57
Condition, (D*)      22
Condition, (E)      138
Condition, (M)      149
Condition, (M1), (M2), (M3), (M4)      24
Condition, (M5)      62
Condition, (SS1)      121
Condition, (SS2)      122
Condition, (SS3)      128 161
Condition, (T), (T'), (T'')      149
conditional probabilities      28 160
Configuration space      3 7 11
Conjugate points      131
Conjugating homeomorphism      131
contour      31
Cover      102
DLR equations      23
Dynamical system, abstract      154
Dynamical system, topological      148
Dynamical system, topologically + transitive      148
Dynamical system, topologically mixing      149
Dynamical system, topologically transitive      149
Energy      4 12
Entropy, mean, or measure theoretic      6 43 103 155 162
Entropy, on finite set      3 42
Entropy, topological      5 115
Equilibrium state      6 40 110 126 163
Ergodic decomposition      39 49 101 159
Ergodic states      see “States ergodic”
Expanding map      138
Expansive $Z^{\nu}$ -action      4 101
Extremal point      151
Face of compact set      157
Flow      162
Flow, Smale      161
Flow, special      163
Fluctuations      49
Function $A_{\Phi}$       34
Function $\psi_>$       81
Generic property      146
Gibbs ensemble      3 13
Gibbs phase rule      49
Gibbs state      7 14 60 133 161
Gibbs state, pure      20
Gibbs state, unique      21
Hard cores      12 68
interactions      12
Interactions, exponentially decreasing      83
Interactions, finite range      34
Interactions, invariant      34
Interactions, pair      55
Interactions, physically equivalent      61
Interactions, space $\mathcal{B}$       57
Interactions, space $\mathcal{B}^{\theta}$       83
Interactions, space $\mathcal{B}_1$       70
Interactions, space $\mathcal{G}$       34
Interactions, space $\mathcal{G}_0$       34
Isomorphism      25
Isomorphism, $Z^{\nu}$ -isomorphism      62
Kolmogorov — Sinai invariant      103 155
Lattice (=Crystal lattice)      7 11 34
Lattice (=ordered set)      146
Lattice gas      11 55 68
Lattice system      24
Lattice system, $Z^{\nu}$ -lattice system      62
Lattice system, mixing      70 78
Lattice system, restriction to a subgroup      64
Lattice system, sum and product      32
Lattice system, transitive      69
Lebesgue number      102
Lebesgue space      154
Limit, thermodynamic      13 14
Limit, Van Hove      43
Linear functional, P-bounded      152

Linear functional, tangent      152
Local product structure      121
Markov partition      124 140
Measure, abstract      154
Measure, Bowen      132
Measure, maximal      158
Measure, probability      153 (see also “State”)
Measureable set      154
Mixture      49
Morphism      24
Morphism, $Z^{\nu}$ -morphism      62
nearest neighbors      63
Non-periodicity      65
Non-wandering point      148
Non-wandering set      124 148
Observable      12
Operator $\mathfrak{L}$       80
Operator $\mathfrak{M}_A$       20
Operator $\mathfrak{S}$       82
Partition      102 155
Partition function      3 35 104 133
Partition function, with periodic boundary condition      90
Partition, $\varepsilon$ -independent      155
Partition, generating      155
Partition, weak Bernoulli      156
Phase, coexistence      53
Phase, mixture      49
Phase, pure thermodynamic      8 49
Phase, rule      49
Phase, transition      8 160
Pressure      4 37 104 126 163
Pressure, relative      115
Pressure, strict convexity of      61
Property      see “Condition”
Pseudo-orbit      123
rectangle      125
Residual set      146
Resultant of measure      157
Separated set      105 162
Set $\Lambda(\alpha)$       36
Shadowing      123
Shub’s entropy conjecture      161
simplex      158
Smale space      121
Space $\mathcal{C}^{\alpha}$       123 126
Space $\mathcal{F}^{\theta}$ , $\mathcal{F}^{\theta}_>$       84
Space of interactions      see “Interactions space”
Spaces $F^{\theta}$ , $F^{\theta}_>$       85
Spanning set      106
Spectral decomposition      124
State      12 101
State, ergodic      39 101 159
State, invariant      39 (see also “Equilibrium state” “Gibbs state”)
Subadditivity      147
Subadditivity, strong      42
Subcover      102
Subshift of finite type      69
Symbol set      125
Symbolic dynamics      125
Symmetry breakdown      8 59
Symmetry group      33
Temperature      4
Theorem, Abramov      163
Theorem, Bishop — Phelps      152
Theorem, central limit      129
Theorem, Dobrushin      160
Theorem, Friedman — Ornstein      156
Theorem, Hahn — Banach      150
Theorem, Israel      50 112 152
Theorem, Krein — Milman      151
Theorem, Lanford — Robinson      152
Theorem, Markov — Kakutani      151
Theorem, Mazur      152
Theorem, Milman      23 152
Theorem, Ornstein      156
Theorem, Parry      133
Theorem, Perron — Frobenius      144
Theorem, separation      151
Thermal equilibrium      4
Thermodynamic formalism      3
Transfer matrix      80
Transition matrix      125
Translation of lattice      34
Translation, invariance      33
Undecidability      65
Upper semi-continuity      147
Vague topology      153
Variational Principle      3 6 45 108 117 163
Wandering point      148
Weak topology      151
Zeta function      89 135 164
“Coarse-grained” quantity      49

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