Mackey M.C. — Time's arrow: the origins of thermodynamic behavior :: Электронная библиотека попечительского совета мехмата МГУ

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Mackey M.C. — Time's arrow: the origins of thermodynamic behavior

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Название: Time's arrow: the origins of thermodynamic behavior

Автор: Mackey M.C.

Аннотация:

Written by a well-known professor of physiology at McGill University, this text presents an informative exploration of the basis of the Second Law of Thermodynamics, detailing the fundamental dynamic properties behind the construction of statistical mechanics. Geared toward physicists and applied mathematicians with an interest in the foundations of statistical mechanics, it is suitable for advanced undergraduate and graduate courses. Unabridged republication of the edition published by Springer-Verlag, New York, 1992.

Язык:

Рубрика: Физика/Термодинамика, статистическая физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 175

Добавлена в каталог: 19.09.2005

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Предметный указатель

$\Gamma$ -space      5
Abstract ergodic theorem      35
Additivity      6 14
Adjoint operators      43 145
Anosov diffeomorphism      59
Anosov flow      60
Asymptotic periodicity      72
Asymptotic periodicity, and correlations      86
Asymptotic periodicity, and entropy      80
Asymptotic periodicity, and ergodicity      74
Asymptotic periodicity, and exactness      96
Asymptotic periodicity, and Keener map      126
Asymptotic periodicity, and perturbations      118 122 126
Asymptotic periodicity, and quadratic map      78
Asymptotic periodicity, and smoothing      71
Asymptotic periodicity, and stationary densities      72
Asymptotic periodicity, and tent map      75 82
Asymptotic periodicity, and Weak Form of Second Law      80
Asymptotic periodicity, conditions for      73 75 84
Asymptotic periodicity, in loosely coupled systems      118
Asymptotic periodicity, in strongly coupled systems      122 123
Asymptotic periodicity, period of      72 125
Average      67
Baker transformation      60
Baker transformation, and additive perturbations      123
Baker transformation, and dyadic transformation      112
Baker transformation, and entropy      64 66 106
Baker transformation, and invertibility      60 113
Baker transformation, and K-systems      67 112
Baker transformation, and Lebesgue measure      60
Baker transformation, and Liouville equation      114
Baker transformation, and microcanonical ensemble      65
Baker transformation, and mixing      60 63
Baker transformation, and trace      112 123
Baker transformation, Frobenius — Perron operator for      64 113
Baker transformation, quadratic      112
Baker transformation, stationary density for      65
Birkhoff ergodic theorem      44
Birkhoff ergodic theorem, extended to ergodic dynamics      53
Blackbody radiation      18
Boltzmann      6 31—33
Boltzmann $\mu$ -space      5
Boltzmann and Loschmidt      32 45
Boltzmann and Zermelo      45
Boltzmann constant      16
Boltzmann equation      114
Boltzmann statistics      16
Boltzmann — Gibbs entropy      5
Boltzmann — Gibbs entropy additivity      6 14
Boltzmann — Gibbs entropy and baker transformation      64 106
Boltzmann — Gibbs entropy and canonical ensemble      11
Boltzmann — Gibbs entropy and conditional entropy      28
Boltzmann — Gibbs entropy and correlations      86
Boltzmann — Gibbs entropy and exactness      100
Boltzmann — Gibbs entropy and grand canonical ensemble      19
Boltzmann — Gibbs entropy and microcanonical ensemble      9
Boltzmann — Gibbs entropy and mixing      64
Boltzmann — Gibbs entropy and quadratic map      28
Boltzmann — Gibbs entropy and tent map      100
Boltzmann — Gibbs entropy and thermodynamic entropy      13
Boltzmann — Gibbs entropy maximal      9 19
Boltzmann — Gibbs entropy sampled      107
Boltzmann — Gibbs entropy uniqueness of      6
Boltzmann — Gibbs entropy, coarse grained      104
canonical ensemble      14
Canonical ensemble and entropy      11 101
Canonical ensemble and exactness      92 94 98 101
Canonical ensemble and mixing      63
Canonical ensemble and stationary density      64
Cauchy — Holder inequality      93
Cesaro convergence      56
Chebyshev inequality      118
Clausius      33
Coarse graining      103
Coarse graining and baker transformation      106
Coarse graining and dynamics      106
Coarse graining and errors      105
Coarse graining and Gibbs      103 106 109
Coarse graining and invertibility      107
Coarse graining and Strong Form of Second Law      107
Coarse graining and trace      113
Coarse graining of densities      104
Coarse graining of entropy      104 105 112
Coarse graining of mixing systems      106
Coarse graining of phase space      103
Coarse graining temporal      107
Conditional entropy      27
Conditional entropy and asymptotic periodicity      80
Conditional entropy and baker transformation      66
Conditional entropy and Boltzmann — Gibbs entropy      28 29
Conditional entropy and correlations      87
Conditional entropy and exactness      98
Conditional entropy and invertible dynamics      31 66
Conditional entropy and Keener map      126
Conditional entropy and Liouville equation      32
Conditional entropy and mixing      64 66
Conditional entropy and ordinary differential equations      32
Conditional entropy and perturbations      119 126 131 149 150
Conditional entropy and quadratic map      78 100
Conditional entropy and tent map      82 95
Conditional entropy and thermodynamic entropy difference      29
Conditional entropy coarse grained      105
Conditional entropy dependence on initial density      80 126
Conditional entropy properties of      29
Conditional entropy sampled      107
Convergence Cesaro      56
Convergence strong      35 92
Convergence weak      35 63
Correlation      67
Correlation and asymptotic periodicity      86
Correlation and entropy      86
Correlation and Frobenius — Perron operator      68
Correlation and Koopman operator      68
Correlation and mixing      68
Covariance      67
Covariance and mixing      68
Covariance normalized      67
Delay differential equation and exactness      91
Delay differential equation and laws of physics      101
density      4
Density and thermodynamic states      4
Density coarse grained      104
Density evolution      43
Density Gaussian      141 151
Density illustrated      4
Density of measure      4
Density stationary      23 38
Diffusion term      145 148
Drift term      145
Dyadic transformation      94
Dyadic transformation and baker transformation      112
Dyadic transformation and exactness      94
Dyadic transformation and Liouville equation      114
Dyadic transformation and microcanonical ensemble      94
Dyadic transformation and noninvertibility      114
Dyadic transformation and perturbations      123
Dyadic transformation and trace      112
Dyadic transformation as a factor      112 114 123
Dyadic transformation Frobenius — Perron operator for      94
Dyadic transformation stationary density for      95
Dynamical system      3
Dynamics and coarse grained entropy      106
Dynamics and Frobenius — Perron operator      39
Dynamics and Koopman operator      43
Dynamics and strong perturbations      120
Dynamics asymptotically periodic      72
Dynamics constructing exact      95
Dynamics ergodic      48
Dynamics exact      89
Dynamics Hamiltonian      33 45 48 101

Dynamics invertible      2
Dynamics irreversible      3
Dynamics loosely coupled to perturbations      117
Dynamics measurable      39
Dynamics measure preserving      41
Dynamics mixing      58
Dynamics noninvertible      3
Dynamics nonsingular      39
Dynamics reversible      2
Dynamics time reversal invariant      2
Dynamics trajectory of      2 110
Dynamics versus perturbations      120
Energy      10 12
Energy and Maxwell — Boltzmann distribution      17
Energy continuous spectrum      17
Energy discrete spectrum      18
Energy Helmholtz      16
Ensemble      5
Entropy and correlations      86
Entropy and dynamics      30
Entropy and invertibility      31
Entropy and mixing      66
Entropy and trace      111
Entropy Boltzmann — Gibbs      5
Entropy coarse grained      104 105 107 114
Entropy conditional      28
Entropy dependence on preparation      80 125
Entropy for baker transformation      64
Entropy for K-systems      67
Entropy for quadratic map      28 78 83 100
Entropy for tent map      82 95
Ergodic theorem abstract      35
Ergodic theorem Birkhoff      44
Ergodic theorem for space and trajectory averages      53
Ergodicity      48
Ergodicity and asymptotic periodicity      74
Ergodicity and Birkhoff theorem      53
Ergodicity and canonical ensemble      54
Ergodicity and Cesaro convergence      56
Ergodicity and Frobenius — Perron operator      52 56
Ergodicity and Hamiltonian dynamics      51
Ergodicity and harmonic oscillator      49
Ergodicity and Koopman operator      51
Ergodicity and Markov operator      57
Ergodicity and microcanonical ensemble      54
Ergodicity and mixing      63
Ergodicity and perturbations      121
Ergodicity and sampled systems      109
Ergodicity and space and time averages      54
Ergodicity and stationary density      52
Ergodicity and tent map      75
Ergodicity and thermodynamic equilibrium      52 54
Ergodicity illustrated      49
Errors      see “Coarse graining; Sampling”
Euler — Bernstein equations      142
Exactness      89
Exactness and asymptotic periodicity      96
Exactness and canonical ensemble      92 94 98 101
Exactness and delay differential equations      91
Exactness and dyadic transformation      94
Exactness and entropy      98 100
Exactness and factors      113
Exactness and invertibility      90
Exactness and K-systems      113
Exactness and Keener map      131
Exactness and lower bound function      97
Exactness and Markov operator      93
Exactness and microcanonical ensemble      94 100
Exactness and partial differential equations      91
Exactness and perturbations      119 122 131 135 149 152 158
Exactness and quadratic map      95 100
Exactness and sampled sequence      108
Exactness and strong convergence      92
Exactness and Strong Form of Second Law      98 100 150 152 158
Exactness and tent map      91 95 96 100
Exactness constructing      95
Exactness convergence rate      96
Exactness illustrated      90
Extension in phase      10
Factor      112
Factor and dyadic transformation      112 114 123
Factor and exactness      113
Factor and K-system      113
Factor and projection operators      113
Factor and quadratic baker transformation      112
Factor and Strong Form of Second Law      113
Factor and trace      112
Fixed point      23
Fokker — Planck equation      22 144
Fokker — Planck equation, and Liouville equation      22 148
Fokker — Planck equation, and Markov operator      22 145 147
Fokker — Planck equation, and noninvertibility      24
Fokker — Planck equation, and stationary density      23 150
Fokker — Planck equation, and thermodynamic equilibrium      150
Fokker — Planck equation, derivation      142
Fokker — Planck equation, generalized solution      146
Frobenius — Perron operator      24 39
Frobenius — Perron operator, and correlations      68
Frobenius — Perron operator, and ergodicity      52 56
Frobenius — Perron operator, and evolution of densities      44
Frobenius — Perron operator, and Koopman operator      44
Frobenius — Perron operator, and Liouville equation      47 114 148
Frobenius — Perron operator, and mixing      63
Frobenius — Perron operator, and ordinary differential equations      23 47 114 148
Frobenius — Perron operator, approximating Markov operators      136
Frobenius — Perron operator, for baker transformation      64 113
Frobenius — Perron operator, for dyadic map      94
Frobenius — Perron operator, for Hamiltonian systems      48
Frobenius — Perron operator, for invertible dynamics      41
Frobenius — Perron operator, for quadratic baker transformation      113
Frobenius — Perron operator, for quadratic map      28 78
Frobenius — Perron operator, for tent map      25 75
Frobenius — Perron operator, properties of      40
Frobenius — Perron operator, stationary density of      23 25
Gas dynamics      61
Gaussian density      141—151
Generalized solution      146
Geodesic flows      62
Gibbs $\gamma$ -space      5
Gibbs and coarse graining      103 106 109
Gibbs and mixing      64
Gibbs extension in phase      10
Gibbs function      16
Gibbs index of probability      5
Gibbs inequality      7
Gibbs inequality, integrated      8
Gibbs microcanonical ensemble      10
God theorem      111
grand canonical ensemble      19
Hamiltonian dynamics      33—45 48 101
Hamiltonian dynamics and ergodicity      51
Hamiltonian dynamics and Frobenius — Perron operator      48
Hamiltonian dynamics and Lebesgue measure      48 101
Hamiltonian dynamics and maximal entropy      101
harmonic oscillator      49
Hat map      see “Tent map”
Helmholtz free energy      16
Index of probability      5
Initial density dependence of entropy on      80 126
Invariant measure      41
Invariant measure, and stationary density      42
Invariant measure, and thermodynamic equilibrium      43
Invariant measure, illustrated      42
Invariant set      48
Invertibility      2
Invertibility and baker transformation      60 113
Invertibility and coarse graining      107
Invertibility and entropy      31 66
Invertibility and exactness      90
Invertibility and laws of physics      101

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