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Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications [Kõva köide]

4.25/5 (8 hinnangut Goodreads-ist)
(School of Chemistry, University of Sydney)
  • Formaat: Hardback, 480 pages, kõrgus x laius x paksus: 254x187x32 mm, kaal: 1034 g, 41 b/w line drawings
  • Ilmumisaeg: 04-Oct-2012
  • Kirjastus: Oxford University Press
  • ISBN-10: 0199662762
  • ISBN-13: 9780199662760
Teised raamatud teemal:
Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and ApplicationsSuurem pilt
  • Formaat: Hardback, 480 pages, kõrgus x laius x paksus: 254x187x32 mm, kaal: 1034 g, 41 b/w line drawings
  • Ilmumisaeg: 04-Oct-2012
  • Kirjastus: Oxford University Press
  • ISBN-10: 0199662762
  • ISBN-13: 9780199662760
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780199662760.html
Märksõnad:
`Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications' builds from basic principles to advanced techniques, and covers the major phenomena, methods, and results of time-dependent systems. It is a pedagogic introduction, a comprehensive reference manual, and an original research monograph. Uniquely, the book treats time-dependent systems by close analogy with their static counterparts, with most of the familiar results of equilibrium thermodynamics and statistical mechanics being generalized and applied to the non-equilibrium case. The book is notable for its unified treatment of thermodynamics, hydrodynamics, stochastic processes, and statistical mechanics, for its self-contained, coherent derivation of a variety of non-equilibrium theorems, and for its quantitative tests against experimental measurements and computer simulations.

Systems that evolve in time are more common than static systems, and yet until recently they lacked any over-arching theory. 'Non-equilibrium Thermodynamics and Statistical Mechanics' is unique in its unified presentation of the theory of non-equilibrium systems, which has now reached the stage of quantitative experimental and computational verification. The novel perspective and deep understanding that this book brings offers the opportunity for new direction and growth in the study of time-dependent phenomena.

'Non-equilibrium Thermodynamics and Statistical Mechanics' is an invaluable reference manual for experts already working in the field. Research scientists from different disciplines will find the overview of time-dependent systems stimulating and thought-provoking. Lecturers in physics and chemistry will be excited by many fresh ideas and topics, insightful explanations, and new approaches. Graduate students will benefit from its lucid reasoning and its coherent approach, as well as from the chem12physof mathematical techniques, derivations, and computer algorithms.
1 Prologue
1(32)
1.1 Entropy and the Second Law
1(3)
1.2 Time Dependent Systems
4(3)
1.2.1 The Second Law is Timeless
5(1)
1.2.2 The Second Entropy
5(2)
1.3 Nature of Probability
7(7)
1.3.1 Frequency
8(1)
1.3.2 Credibility
9(2)
1.3.3 Measure
11(1)
1.3.4 Determination of Randomness
12(2)
1.4 States, Entropy, and Probability
14(12)
1.4.1 Macrostates and Microstates
14(1)
1.4.2 Weight and Probability
15(2)
1.4.3 Entropy
17(3)
1.4.4 Transitions and the Second Entropy
20(5)
1.4.5 The Continuum
25(1)
1.5 Reservoirs
26(7)
1.5.1 Equilibrium Systems
27(2)
1.5.2 Non-Equilibrium Steady State
29(4)
2 Fluctuation Theory
33(28)
2.1 Gaussian Probability
33(5)
2.2 Exponential Decay in Markovian Systems
38(4)
2.3 Small Time Expansion
42(3)
2.4 Results for Pure Parity Systems
45(6)
2.4.1 Onsager Regression Hypothesis and Reciprocal Relations
45(1)
2.4.2 Green-Kubo Expression
46(1)
2.4.3 Physical Interpretation of the Second Entropy
47(1)
2.4.4 The Dissipation
48(1)
2.4.5 Stability Theory
48(2)
2.4.6 Non-Reversibility of the Trajectory
50(1)
2.4.7 Third Entropy
50(1)
2.5 Fluctuations of Mixed Time Parity
51(10)
2.5.1 Second Entropy and Time Correlation Functions
51(3)
2.5.2 Small Time Expansion for the General Case
54(4)
2.5.3 Magnetic Fields and Coriolis Forces
58(3)
3 Brownian Motion
61(36)
3.1 Gaussian, Markov Processes
63(1)
3.2 Free Brownian Particle
64(2)
3.3 Pinned Brownian Particle
66(2)
3.4 Diffusion Equation
68(1)
3.5 Time Correlation Functions
69(2)
3.6 Non-Equilibrium Probability Distribution
71(12)
3.6.1 Stationary Trap
71(1)
3.6.2 Uniformly Moving Trap
72(4)
3.6.3 Mixed Parity Formulation of the Moving Trap
76(7)
3.7 Entropy, Probability, and their Evolution
83(14)
3.7.1 Time Evolution of the Entropy and Probability
83(4)
3.7.2 Compressibility of the Equations of Motion
87(1)
3.7.3 The Fokker-Planck Equation
88(3)
3.7.4 Generalised Equipartition Theorem
91(2)
3.7.5 Liouville's Theorem
93(4)
4 Heat Conduction
97(24)
4.1 Equilibrium System
97(2)
4.2 First Energy Moment and First Temperature
99(2)
4.3 Second Entropy
101(2)
4.4 Thermal Conductivity and Energy Correlations
103(1)
4.5 Reservoirs
104(6)
4.5.1 First Entropy
105(2)
4.5.2 Second Entropy
107(3)
4.6 Heat and Number Flow
110(1)
4.7 Heat and Current Flow
111(10)
5 Second Entropy for Fluctuating Hydrodynamics
121(24)
5.1 Conservation Laws
122(6)
5.1.1 Densities, Velocities, and Chemical Reactions
122(1)
5.1.2 Number Flux
123(2)
5.1.3 Energy Flux
125(2)
5.1.4 Linear Momentum
127(1)
5.2 Entropy Density and its Rate of Change
128(5)
5.2.1 Sub-system Dissipation
131(2)
5.2.2 Steady State
133(1)
5.3 Second Entropy
133(6)
5.3.1 Variational Principle
137(1)
5.3.2 Flux Optimisation
137(2)
5.4 Navier-Stokes and Energy Equations
139(6)
6 Heat Convection and Non-Equilibrium Phase Transitions
145(28)
6.1 Hydrodynamic Equations of Convection
146(4)
6.1.1 Boussinesq Approximation
146(1)
6.1.2 Conduction
147(1)
6.1.3 Convection
148(2)
6.2 Total First Entropy of Convection
150(4)
6.3 Algorithm for Ideal Straight Rolls
154(3)
6.3.1 Hydrodynamic Equations
154(1)
6.3.2 Fourier Expansion
154(3)
6.3.3 Nusselt Number
157(1)
6.4 Algorithm for the Cross Roll State
157(4)
6.4.1 Hydrodynamic Equations and Conditions
157(2)
6.4.2 Fourier Expansion
159(2)
6.5 Algorithm for Convective Transitions
161(2)
6.6 Convection Theory and Experiment
163(10)
7 Equilibrium Statistical Mechanics
173(60)
7.1 Hamilton's Equations of Motion
174(2)
7.1.1 Classical versus Quantum Statistical Mechanics
176(1)
7.2 Probability Density of an Isolated System
176(10)
7.2.1 Ergodic Hypothesis
177(1)
7.2.2 Time, Volume, and Surface Averages
177(3)
7.2.3 Energy Uniformity
180(2)
7.2.4 Trajectory Uniformity
182(2)
7.2.5 Partition Function and Entropy
184(2)
7.2.6 Internal Entropy of Phase Space Points
186(1)
7.3 Canonical Equilibrium System
186(9)
7.3.1 Maxwell-Boltzmann Distribution
186(2)
7.3.2 Helmholtz Free Energy
188(4)
7.3.3 Probability Distribution for Other Systems
192(2)
7.3.4 Equipartition Theorem
194(1)
7.4 Transition Probability
195(15)
7.4.1 Stochastic Equations of Motion
195(3)
7.4.2 Second Entropy
198(5)
7.4.3 Mixed Parity Derivation of the Second Entropy and the Equations of Motion
203(2)
7.4.4 Irreversibility and Dissipation
205(2)
7.4.5 The Fokker-Planck Equation and Stationarity of the Equilibrium Probability
207(3)
7.5 Evolution in Phase Space
210(8)
7.5.1 Various Phase Functions
210(4)
7.5.2 Compressibility
214(2)
7.5.3 Liouville's Theorem
216(2)
7.6 Reversibility
218(8)
7.6.1 Isolated System
219(1)
7.6.2 Canonical Equilibrium System
220(6)
7.7 Trajectory Probability and Time Correlation Functions
226(7)
7.7.1 Trajectory Probability
226(1)
7.7.2 Equilibrium Averages
227(1)
7.7.3 Time Correlation Functions
227(2)
7.7.4 Reversibility
229(4)
8 Non-Equilibrium Statistical Mechanics
233(62)
8.1 General Considerations
233(2)
8.2 Reservoir Entropy
235(5)
8.2.1 Trajectory Entropy
235(2)
8.2.2 Reduction to the Point Entropy
237(2)
8.2.3 Fluctuation Form for the Reservoir Entropy
239(1)
8.3 Transitions and Motion in Phase Space
240(22)
8.3.1 Foundations for Time Dependent Weight
240(4)
8.3.2 Fluctuation Form of the Second Entropy
244(3)
8.3.3 Time Correlation Function
247(2)
8.3.4 Stochastic, Dissipative Equations of Motion
249(9)
8.3.5 Transition Probability and Fokker-Planck Equation
258(2)
8.3.6 Most Likely Force with Constraints
260(2)
8.4 Changes in Entropy and Time Derivatives
262(13)
8.4.1 Change in Entropy
262(4)
8.4.2 Irreversibility and Dissipation
266(2)
8.4.3 Various Time Derivatives
268(5)
8.4.4 Steady State System
273(2)
8.5 Odd Projection of the Dynamic Reservoir Entropy
275(5)
8.6 Path Entropy and Transitions
280(9)
8.6.1 Path Entropy
280(7)
8.6.2 Fluctuation and Work Theorem
287(2)
8.7 Path Entropy for Mechanical Work
289(6)
8.7.1 Evolution of the Reservoir Entropy and Transitions
289(3)
8.7.2 Transition Theorems
292(3)
9 Statistical Mechanics of Steady Flow: Heat and Shear
295(34)
9.1 Thermodynamics of Steady Heat Flow
295(8)
9.1.1 Canonical Equilibrium System
295(1)
9.1.2 Fourier's Law of Heat Conduction
296(3)
9.1.3 Second Entropy for Heat Flow
299(4)
9.2 Phase Space Probability Density
303(5)
9.2.1 Explicit Hamiltonian and First Energy Moment
303(3)
9.2.2 Reservoir Entropy and Probability Density
306(2)
9.3 Most Likely Trajectory
308(2)
9.4 Equipartition Theorem for Heat Flow
310(3)
9.5 Green-Kubo Expressions for the Thermal Conductivity
313(7)
9.5.1 Isolated System
313(2)
9.5.2 Heat Reservoirs
315(3)
9.5.3 Relation with Odd Projection
318(2)
9.6 Shear Flow
320(9)
9.6.1 Second Entropy for Shear Flow
322(1)
9.6.2 Phase Space Probability Density
323(3)
9.6.3 Most Likely Trajectory
326(1)
9.6.4 Equipartition Theorem
327(2)
10 Generalised Langevin Equation
329(60)
10.1 Free Brownian Particle
331(11)
10.1.1 Time Correlation Functions
332(3)
10.1.2 Mixed Parity Digression
335(2)
10.1.3 Diffusion Constant
337(1)
10.1.4 Trajectory Entropy and Correlation
338(4)
10.2 Langevin and Smoluchowski Equations
342(1)
10.3 Perturbation Theory
343(13)
10.3.1 Most Likely Velocity
343(4)
10.3.2 Alternative Derivation
347(1)
10.3.3 Most Likely Position
348(1)
10.3.4 Stochastic Dissipative Equations of Motion
348(3)
10.3.5 Generalised Langevin Equation for Velocity
351(2)
10.3.6 Fluctuation Dissipation Theorem
353(1)
10.3.7 Weiner-Khintchine Theorem
354(1)
10.3.8 Exponentially Decaying Memory Function
355(1)
10.4 Adiabatic Linear Response Theory
356(2)
10.5 Numerical Results for a Brownian Particle in a Moving Trap
358(8)
10.5.1 Langevin Theory
359(1)
10.5.2 Smoluchowski Theory
360(1)
10.5.3 Computer Simulations
360(1)
10.5.4 Perturbation Algorithm
361(1)
10.5.5 Relative Amplitude and Phase Lag
361(3)
10.5.6 Stochastic Trajectory
364(2)
10.6 Generalised Langevin Equation in the Case of Mixed Parity
366(12)
10.6.1 Equilibrium System
366(5)
10.6.2 Regression of Fluctuation
371(2)
10.6.3 Time Dependent Perturbation
373(4)
10.6.4 Generalised Langevin Equation
377(1)
10.7 Projector Operator Formalism
378(5)
10.8 Harmonic Oscillator Model for the Memory Function
383(6)
10.8.1 Generalised Langevin Equation
384(3)
10.8.2 Modified Random Force
387(1)
10.8.3 Discussion
388(1)
11 Non-Equilibrium Computer Simulation Algorithms
389(62)
11.1 Stochastic Molecular Dynamics
391(18)
11.1.1 Equilibrium Systems
391(4)
11.1.2 Mechanical Non-Equilibrium System
395(1)
11.1.3 Driven Brownian Motion
396(4)
11.1.4 Steady Heat Flow
400(9)
11.2 Non-Equilibrium Monte Carlo
409(26)
11.2.1 Equilibrium Systems
409(3)
11.2.2 Non-Equilibrium Systems
412(5)
11.2.3 Driven Brownian Motion
417(12)
11.2.4 Steady Heat Flow
429(6)
11.3 Brownian Dynamics
435(16)
11.3.1 Elementary Brownian Dynamics
437(3)
11.3.2 Perturbative Brownian Dynamics
440(5)
11.3.3 Stochastic Calculus
445(6)
References 451(4)
Index 455
Dr Attard is a research scientist working in the fields of thermodynamics and statistical mechanics. He is recently retired as a Professorial Research Fellow at the School of Chemistry, the University of Sydney. He has been awarded a Queen Elizabeth II Fellowship by the Australian Research Council, and has held academic positions at universities in Australia, Europe, and North America.