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

Invertibility and Liouville equation      24 114
Invertibility and Markov operator      23
Invertibility and mixing      60
Irreversible      see “Noninvertible”
Ito calculus      141
Jensen inequality      30
K-systems      66
K-systems and baker transformation      67 112
K-systems and entropy      67
K-systems and exactness      113
K-systems and factors      113
K-systems and mixing      67
K-systems and traces      112
Keener map      126
Keener map and entropy      126
Keener map and perturbations      126
Keener map asymptotic periodicity in      126
Keener map exactness in      13
Kolmogorov equation      144 145
Koopman operator      43
Koopman operator and correlations      68
Koopman operator and ergodicity      51
Koopman operator and evolution of densities      44
Koopman operator and Frobenius — Perron operator      44
Koopman operator and ordinary differential equations      46
Koopman operator and time averages      43
KRYLOV      64
Landau equation      153
laws of physics      101
Lebesgue measure      4 42
Lebesgue measure and baker transformation      60
Lebesgue measure and Hamiltonian systems      48 101
Lebesgue measure and microcanonical ensemble      9 42 54 63 94 100
Lebesgue measure and mixing      60
Lebesgue measure and quadratic map      42
Lebesgue measure and Radon — Nikodym theorem      26
Lebesgue measure and tent map      91
Liapunov function      122 148
Liouville equation      22 47
Liouville equation and baker transformation      114
Liouville equation and dyadic transformation      114
Liouville equation and entropy      32
Liouville equation and Fokker — Planck equation      22 148
Liouville equation and Frobenius — Perron operator      47 114 148
Liouville equation and invertibility      24 114
Liouville equation and perturbations      148
Liouville theorem      47
Loschmidt      32 45
Lower bound function      97
Markov operator      22
Markov operator, and Fokker — Planck equation      22 145 147
Markov operator, and stochastic differential equations      22 147
Markov operator, approximated by Frobenius — Perron operators      136
Markov operator, asymptotically periodic      72
Markov operator, ergodic      57
Markov operator, exact      93
Markov operator, fixed point of      23
Markov operator, from perturbations      117 119 120 124 131
Markov operator, invertible      23
Markov operator, mixing      64
Markov operator, noninvertible      24
Markov operator, properties      23
Markov operator, smoothing      70
Markov operator, stationary density of      23 38
Maximal entropy and blackbody radiation      18
Maximal entropy and canonical ensemble      11 101
Maximal entropy and grand canonical ensemble      19
Maximal entropy and Hamiltonian dynamics      101
Maximal entropy and Maxwell — Boltzmann distribution      17
Maximal entropy and microcanonical ensemble      9
Maximal entropy and thermodynamic equilibrium      12
Maxwell — Boltzmann distribution continuous      17
Maxwell — Boltzmann distribution discrete      18
Measurable transformation      39
Measure      4
Measure and density      4
Measure illustrated      4 42
Measure invariant      41
Measure Lebesgue      4 42
Measure preserving transformation      41
Measure space      1
Measure space $\sigma$ -finite      2
Measure space and thermodynamic systems      2
Metric indecomposability      see “Ergodic”
Metric transitivity      see “Ergodic”
microcanonical ensemble      9
Microcanonical ensemble and baker transformation      65
Microcanonical ensemble and Boltzmann — Gibbs entropy      9
Microcanonical ensemble and dyadic transformation      94
Microcanonical ensemble and ergodicity      54
Microcanonical ensemble and exactness      94—100
Microcanonical ensemble and Gibbs      10
Microcanonical ensemble and Lebesgue measure      9 42 54 63 94 100
Microcanonical ensemble and maximal entropy      9
Microcanonical ensemble and stationary density      54 64
Microcanonical ensemble density of      10
Mixing      59
Mixing $\mu$ -space      5
Mixing and baker transformation      60 63
Mixing and canonical ensemble      63
Mixing and coarse graining      106
Mixing and correlations      68
Mixing and covariance      67
Mixing and entropy      64 66
Mixing and ergodicity      63
Mixing and Frobenius — Perron operator      63
Mixing and geodesic flows      62
Mixing and Gibbs      64
Mixing and invertibility      60
Mixing and K-systems      67
Mixing and Lebesgue measure      60
Mixing and perturbations      121
Mixing and sampling      108
Mixing and weak convergence      63
Mixing gas model      61
Mixing illustrated      59
Mixing Markov operator      64
Noise      see “Perturbations”
Noninvertibility      3
Noninvertibility and Boltzmann equation      114
Noninvertibility and conditional entropy      33
Noninvertibility and dyadic transformation      114
Noninvertibility and exactness      90
Noninvertibility and Fokker — Planck equation      24
Noninvertibility and laws of physics      101
Noninvertibility and Markov operators      24
Nonsingular transformation      39
Normalized covariance      67
Observable      5
Observable and canonical ensemble      11
Observable and grand canonical ensemble      19
Observable and maximal entropy      12
Observable and Maxwell — Boltzmann distribution      16
Ordinary differential equations and conditional entropy      32 45
Ordinary differential equations and density evolution      22
Ordinary differential equations and Frobenius — Perron operator      23 47 114 148
Ordinary differential equations and Koopman operator      46
Ordinary differential equations and Liouville equation      22 48
Ordinary differential equations and perturbations      140
Ordinary differential equations Hamiltonian system      33 45 48 101
Partial differential equations and exactness      91
Partition      103
Partition function      12
Perturbations additive      121 123 153 155
Perturbations and asymptotic periodicity      118 122 126
Perturbations and baker transformation      123
Perturbations and dyadic transformation      123
Perturbations and dynamics      115
Perturbations and entropy      119 126 131 149 150
Perturbations and ergodicity      121

Perturbations and exactness      119 122 131 149 152 158
Perturbations and Liouville equation      148
Perturbations and mixing      121
Perturbations and phase transitions      151
Perturbations and stationary density      119 125 150 152 153
Perturbations and strong form of Second law      119 122 131 135 149 150
Perturbations and thermodynamic equilibrium      119 125
Perturbations and traces      119 121
Perturbations and weak form of Second law      118 122 123 124 126 133
Perturbations by other systems      119 121
Perturbations of Keener map      126
Perturbations of ordinary differential equations      139
Perturbations parametric      131 156
Perturbations versus dynamics      120 121
Phase space      1
Phase space coarse grained      103
Phase transitions first order      155 157
Phase transitions second order      154 158
Planck blackbody radiatiori      18
Poincare recurrence theorem      45
Poincare recurrence theorem extension      55
Probability current      152
Projection operator      113
Quadratic baker transformation      112
Quadratic baker transformation and factors      112
Quadratic baker transformation and trace      112
Quadratic baker transformation Frobenius — Perron operator for      113
Quadratic baker transformation stationary density for      113
Quadratic map      27
Quadratic map and asymptotic periodicity      78 83
Quadratic map and entropy      28 78 83 100
Quadratic map and tent map      27
Quadratic map as factor      113
Quadratic map exactness of      95 100
Quadratic map Frobenius — Perron operator for      28 78
Quadratic map invariant measure for      42
Quadratic map stationary density for      28 42
Quantized behavior      72
Radon — Nikodym theorem      26
Rayliegh — Jeans radiation law      19
Recurrence      45
Recurrence theorem      45 54
Recurrent point      45
Reversibility      see “Invertibility”
Sampling      107
Sampling and entropy      109
Sampling and ergodicity      109
Sampling and exactness      108
Sampling and mixing      108
Sampling illustrated      108
Scalar product      35
Second law of thermodynamics      see “Strong Form of Second Law of Thermodynamics; Weak Form of Second Law of Thermodynamics”
Semidynamical system      3
Semidynamical system $\sigma$ -algebra      1
Semidynamical system $\sigma$ -finite measure space      2
Smoothing operator      70
Spatial averages convergence      96
Spatial averages in ergodic systems      54
Spectral decomposition theorem      71
Stationary density      23 38
Stationary density and asymptotic periodicity      72
Stationary density and canonical ensemble      64
Stationary density and ergodicity      52
Stationary density and invariant measures      42
Stationary density and microcanonical ensemble      54 64
Stationary density and perturbations      119 125 150 152 153
Stationary density and thermodynamic equilibrium      4 23 34 42 52
Stationary density for baker transformation      65
Stationary density for dyadic map      95
Stationary density for Fokker — Planck equation      23 150
Stationary density for Frobenius — Perron operator      23 25
Stationary density for quadratic baker transformation      113
Stationary density for quadratic map      28 42
Stationary density for tent map      25 76
Stochastic differential equations      22 141
Stochastic differential equations and Markov operators      22 147
Stochastic differential equations and phase transitions      151
Stochastic differential equations Fokker — Planck equation for      22 144
Stochastic kernel      117
Stratonovich calculus      141
Strong convergence      35
Strong convergence and exactness      92
Strong convergence and thermodynamic equilibrium      36
Strong Form of Second Law of Thermodynamics      ix
Strong Form of Second Law of Thermodynamics and coarse graining      107
Strong Form of Second Law of Thermodynamics and exactness      98 100 150 152 158
Strong Form of Second Law of Thermodynamics and factors      113
Strong Form of Second Law of Thermodynamics and global stability      13
Strong Form of Second Law of Thermodynamics and laws of physics      101
Strong Form of Second Law of Thermodynamics and perturbations      119 121 131 135 149 150
System state density averages      34
Temperature      13
Temporal coarse graining      see “Sampling”
Tent map      24
Tent map and asymptotic periodicity      75 82
Tent map and entropy      82 95 100
Tent map and exactness      91 95 96 100
Tent map and Lebesgue measure      91
Tent map and quadratic map      27
Tent map and stationary density      25 76
Tent map and Weak Form of Second Law of Thermodynamics      83
Tent map ergodicity of      75
Tent map Frobenius — Perron operator for      25 75
Tent map stationary density for      25 76
Thermodynamic entropy      ix 12 13
Thermodynamic entropy and Boltzmann — Gibbs entropy      13
Thermodynamic entropy difference      ix
Thermodynamic entropy difference and conditional entropy      29
Thermodynamic equilibria      ix 13
Thermodynamic equilibria and ergodicity      52
Thermodynamic equilibria and Fokker — Planck equation      150
Thermodynamic equilibria and invariant measures      43
Thermodynamic equilibria and maximal entropy      12
Thermodynamic equilibria and perturbations      119 125
Thermodynamic equilibria and stationary density      4 23 34 42 52
Thermodynamic equilibria and strong convergence      36
Thermodynamic equilibria and upper bound function      36
Thermodynamic equilibria and weak convergence      35
Thermodynamic equilibria and weak precompactness      36
Thermodynamic equilibria conditions for existence      34
Thermodynamic equilibria global      13
Thermodynamic equilibria metastable      13
Thermodynamic limit      5
Thermodynamic state      4
Thermodynamic system      4
Thermodynamic system and density      4
Thermodynamic system and measure space      2
Thermodynamic system state of      4
Time reversal invariance      see “Invertibility”
Trace      110
Trace and baker transformation      112 123
Trace and coarse grained entropy      113
Trace and dyadic transformation      112
Trace and entropy      111
Trace and factor      112
Trace and God theorem      111
Trace and K-systems      112
Trace and perturbations      119 121
Trace and quadratic baker transformation      112
Trace and trajectories      110
Trajectories      2 110
Trajectories average along      43 54
Trajectories average along and trace      110
Trajectories average along convergence of      96
Transient operator      71
Trivial invariant set      48
Uniform parabolicity condition      143
Voigts theorem      30
Weak convergence      35
Weak convergence and existence of equilibria      35

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