Non-equilibrium thermodynamics and statistical mechanics : foundations and applications /

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'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, an...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Attard, Phil (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford : Oxford University Press, ©2012.
Temas:
Nonequilibrium thermodynamics.
Statistical mechanics.
Stochastic processes.
Stochastic Processes
Thermodynamique irréversible.
Mécanique statistique.
Processus stochastiques.
SCIENCE > Mechanics > Thermodynamics.
Popular Science.
Nonequilibrium thermodynamics
Statistical mechanics
Nichtgleichgewichtsthermodynamik
Statistische Mechanik
Termodynamik.
Statistisk mekanik.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover Page
  • Title Page
  • Copyright Page
  • Preface
  • Contents
  • Detailed Contents
  • Chapter 1 Prologue
  • 1.1 Entropy and the Second Law
  • 1.2 Time Dependent Systems
  • 1.2.1 The Second Law is Timeless
  • 1.2.2 The Second Entropy
  • 1.3 Nature of Probability
  • 1.3.1 Frequency
  • 1.3.2 Credibility
  • 1.3.3 Measure
  • 1.3.4 Determination of Randomness
  • 1.4 States, Entropy, and Probability
  • 1.4.1 Macrostates and Microstates
  • 1.4.2 Weight and Probability
  • 1.4.3 Entropy
  • 1.4.4 Transitions and the Second Entropy
  • 1.4.5 The Continuum
  • 1.5 Reservoirs
  • 1.5.1 Equilibrium Systems
  • 1.5.2 Non-Equilibrium Steady State
  • Chapter 2 Fluctuation Theory
  • 2.1 Gaussian Probability
  • 2.2 Exponential Decay in Markovian Systems
  • 2.3 Small Time Expansion
  • 2.4 Results for Pure Parity Systems
  • 2.4.1 Onsager Regression Hypothesis and Reciprocal Relations
  • 2.4.2 Green-Kubo Expression
  • 2.4.3 Physical Interpretation of the Second Entropy
  • 2.4.4 The Dissipation
  • 2.4.5 Stability Theory
  • 2.4.6 Non-Reversibility of the Trajectory
  • 2.4.7 Third Entropy
  • 2.5 Fluctuations of Mixed Time Parity
  • 2.5.1 Second Entropy and Time Correlation Functions
  • 2.5.2 Small Time Expansion for the General Case
  • 2.5.3 Magnetic Fields and Coriolis Forces
  • Chapter 3 Brownian Motion
  • 3.1 Gaussian, Markov Processes
  • 3.2 Free Brownian Particle
  • 3.3 Pinned Brownian Particle
  • 3.4 Diffusion Equation
  • 3.5 Time Correlation Functions
  • 3.6 Non-Equilibrium Probability Distribution
  • 3.6.1 Stationary Trap
  • 3.6.2 Uniformly Moving Trap
  • 3.6.3 Mixed Parity Formulation of the Moving Trap
  • 3.7 Entropy Probability, and their Evolution
  • 3.7.1 Time Evolution of the Entropy and Probability
  • 3.7.2 Compressibility of the Equations of Motion
  • 3.7.3 The Fokker-Planck Equation
  • 3.7.4 Generalised Equipartition Theorem
  • 3.7.5 Liouville's Theorem.
  • Chapter 4 Heat Conduction
  • 4.1 Equilibrium System
  • 4.2 First Energy Moment and First Temperature
  • 4.3 Second Entropy
  • 4.4 Thermal Conductivity and Energy Correlations
  • 4.5 Reservoirs
  • 4.5.1 First Entropy
  • 4.5.2 Second Entropy
  • 4.6 Heat and Number Flow
  • 4.7 Heat and Current Flow
  • Chapter 5 Second Entropy for Fluctuating Hydrodynamics
  • 5.1 Conservation Laws
  • 5.1.1 Densities, Velocities, and Chemical Reactions
  • 5.1.2 Number Flux
  • 5.1.3 Energy Flux
  • 5.1.4 Linear Momentum
  • 5.2 Entropy Density and its Rate of Change
  • 5.2.1 Sub-system Dissipation
  • 5.2.2 Steady State
  • 5.3 Second Entropy
  • 5.3.1 Variational Principle
  • 5.3.2 Flux Optimisation
  • 5.4 Navier-Stokes and Energy Equations
  • Chapter 6 Heat Convection and Non-Equilibrium Phase Transitions
  • 6.1 Hydrodynamic Equations of Convection
  • 6.1.1 Boussinesq Approximation
  • 6.1.2 Conduction
  • 6.1.3 Convection
  • 6.2 Total First Entropy of Convection
  • 6.3 Algorithm for Ideal Straight Rolls
  • 6.3.1 Hydrodynamic Equations
  • 6.3.2 Fourier Expansion
  • 6.3.3 Nusselt Number
  • 6.4 Algorithm for the Cross Roll State
  • 6.4.1 Hydrodynamic Equations and Conditions
  • 6.4.2 Fourier Expansion
  • 6.5 Algorithm for Convective Transitions
  • 6.6 Convection Theory and Experiment
  • Chapter 7 Equilibrium Statistical Mechanics
  • 7.1 Hamilton's Equations of Motion
  • 7.1.1 Classical versus Quantum Statistical Mechanics
  • 7.2 Probability Density of an Isolated System
  • 7.2.1 Ergodic Hypothesis
  • 7.2.2 Time, Volume, and Surface Averages
  • 7.2.3 Energy Uniformity
  • 7.2.4 Trajectory Uniformity
  • 7.2.5 Partition Function and Entropy
  • 7.2.6 Internal Entropy of Phase Space Points
  • 7.3 Canonical Equilibrium System
  • 7.3.1 Maxwell-Boltzmann Distribution
  • 7.3.2 Helmholtz Free Energy
  • 7.3.3 Probability Distribution for Other Systems
  • 7.3.4 Equipartition Theorem.
  • 7.4 Transition Probability
  • 7.4.1 Stochastic Equations of Motion
  • 7.4.2 Second Entropy
  • 7.4.3 Mixed Parity Derivation of the Second Entropy and the Equations of Motion
  • 7.4.4 Irreversibility and Dissipation
  • 7.4.5 The Fokker-Planck Equation and Stationarity of the Equilibrium Probability
  • 7.5 Evolution in Phase Space
  • 7.5.1 Various Phase Functions
  • 7.5.2 Compressibility
  • 7.5.3 Liouville's Theorem
  • 7.6 Reversibility
  • 7.6.1 Isolated System
  • 7.6.2 Canonical Equilibrium System
  • 7.7 Trajectory Probability and Time Correlation Functions
  • 7.7.1 Trajectory Probability
  • 7.7.2 Equilibrium Averages
  • 7.7.3 Time Correlation Functions
  • 7.7.4 Reversibility
  • Chapter 8 Non-Equilibrium Statistical Mechanics
  • 8.1 General Considerations
  • 8.2 Reservoir Entropy
  • 8.2.1 Trajectory Entropy
  • 8.2.2 Reduction to the Point Entropy
  • 8.2.3 Fluctuation Form for the Reservoir Entropy
  • 8.3 Transitions and Motion in Phase Space
  • 8.3.1 Foundations for Time Dependent Weight
  • 8.3.2 Fluctuation Form of the Second Entropy
  • 8.3.3 Time Correlation Function
  • 8.3.4 Stochastic, Dissipative Equations of Motion
  • 8.3.5 Transition Probability and Fokker-Planck Equation
  • 8.3.6 Most Likely Force with Constraints
  • 8.4 Changes in Entropy and Time Derivatives
  • 8.4.1 Change in Entropy
  • 8.4.2 Irreversibility and Dissipation
  • 8.4.3 Various Time Derivatives
  • 8.4.4 Steady State System
  • 8.5 Odd Projection of the Dynamic Reservoir Entropy
  • 8.6 Path Entropy and Transitions
  • 8.6.1 Path Entropy
  • 8.6.2 Fluctuation and Work Theorem
  • 8.7 Path Entropy for Mechanical Work
  • 8.7.1 Evolution of the Reservoir Entropy and Transitions ...
  • 8.7.2 Transition Theorems
  • Chapter 9 Statistical Mechanics of Steady Flow: Heat and Shear
  • 9.1 Thermodynamics of Steady Heat Flow
  • 9.1.1 Canonical Equilibrium System.
  • 9.1.2 Fourier's Law of Heat Conduction
  • 9.1.3 Second Entropy for Heat Flow
  • 9.2 Phase Space Probability Density
  • 9.2.1 Explicit Hamiltonian and First Energy Moment
  • 9.2.2 Reservoir Entropy and Probability Density
  • 9.3 Most Likely Trajectory
  • 9.4 Equipartition Theorem for Heat Flow
  • 9.5 Green-Kubo Expressions for the Thermal Conductivity
  • 9.5.1 Isolated System
  • 9.5.2 Heat Reservoirs
  • 9.5.3 Relation with Odd Projection
  • 9.6 Shear Flow
  • 9.6.1 Second Entropy for Shear Flow
  • 9.6.2 Phase Space Probability Density
  • 9.6.3 Most Likely Trajectory
  • 9.6.4 Equipartition Theorem
  • Chapter 10 Generalised Langevin Equation
  • 10.1 Free Brownian Particle
  • 10.1.1 Time Correlation Functions
  • 10.1.2 Mixed Parity Digression
  • 10.1.3 Diffusion Constant
  • 10.1.4 Trajectory Entropy and Correlation
  • 10.2 Langevin and Smoluchowski Equations
  • 10.3 Perturbation Theory
  • 10.3.1 Most Likely Velocity
  • 10.3.2 Alternative Derivation
  • 10.3.3 Most Likely Position
  • 10.3.4 Stochastic Dissipative Equations of Motion
  • 10.3.5 Generalised Langevin Equation for Velocity
  • 10.3.6 Fluctuation Dissipation Theorem
  • 10.3.7 Weiner-Khintchine Theorem
  • 10.3.8 Exponentially Decaying Memory Function
  • 10.4 Adiabatic Linear Response Theory
  • 10.5 Numerical Results for a Brownian Particle in a Moving Trap
  • 10.5.1 Langevin Theory
  • 10.5.2 Smoluchowski Theory
  • 10.5.3 Computer Simulations
  • 10.5.4 Perturbation Algorithm
  • 10.5.5 Relative Amplitude and Phase Lag
  • 10.5.6 Stochastic Trajectory
  • 10.6 Generalised Langevin Equation in the Case of Mixed Parity
  • 10.6.1 Equilibrium System
  • 10.6.2 Regression of Fluctuation
  • 10.6.3 Time Dependent Perturbation
  • 10.6.4 Generalised Langevin Equation
  • 10.7 Projector Operator Formalism
  • 10.8 Harmonic Oscillator Model for the Memory Function
  • 10.8.1 Generalised Langevin Equation.
  • 10.8.2 Modified Random Force
  • 10.8.3 Discussion
  • Chapter 11 Non-Equilibrium Computer Simulation Algorithms
  • 11.1 Stochastic Molecular Dynamics
  • 11.1.1 Equilibrium Systems
  • 11.1.2 Mechanical Non-Equilibrium System
  • 11.1.3 Driven Brownian Motion
  • 11.1.4 Steady Heat Flow
  • 11.2 Non-Equilibrium Monte Carlo
  • 11.2.1 Equilibrium Systems
  • 11.2.2 Non-Equilibrium Systems
  • 11.2.3 Driven Brownian Motion
  • 11.2.4 Steady Heat Flow
  • 11.3 Brownian Dynamics
  • 11.3.1 Elementary Brownian Dynamics
  • 11.3.2 Perturbative Brownian Dynamics
  • 11.3.3 Stochastic Calculus
  • References
  • Index
  • Footnotes.

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