The importance of thermodynamics, particularly its Second Principle, to all branches of science in which systems with very large numbers of particles are involved cannot be overstated. This book offers a panoramic view of non-equilibrium thermodynamics. Perhaps the two most attractive aspects of thermodynamic equilibrium are its stability and its independence from the specifics of the particular system involved. Does an equivalent exist for non-equilibrium thermodynamics? Many researchers have tried to describe such stability in the same way that the Second Principle describes the stability of thermodynamic equilibrium - and failed. Most of them invoked either entropy, or its production rate, or some modified version of it. In their efforts, however, those researchers have found a lot of useful stability criteria for far-from-equilibrium states. These criteria usually take the form of variational principles, in terms of the minimization or maximization of some quantity. The aim of this book is to discuss these variational principles by highlighting the role of macroscopic quantities. This book is aimed at a wider audience than those most often exposed to the criteria described, i.e., undergraduates in STEM, as well as the usual interested and invested professionals.
Author(s): Andrea Di Vita
Series: Lecture Notes in Physics, 1007
Publisher: Springer
Year: 2022
Language: English
Pages: 238
City: Cham
Preface
Contents
List of Main Variables and Acronyms
Latin
Greek
Acronyms
1 Looking for the Holy Grail?
2 Thermodynamic Equilibrium
2.1 Some Fundamental Concepts
2.2 A Minimum Amount of Work
2.3 Thermodynamic Potentials
2.4 The Impact of Magnetic Field
2.5 A Symmetry
3 Local Thermodynamic Equilibrium
3.1 Le Châtelier's Principle
3.2 Local Thermodynamic Equilibrium and Le Châtelier's Principle
3.3 Some Consequences of Local Thermodynamic Equilibrium
3.4 The Role of Gravity
3.4.1 Collapse
3.4.2 Constant Gravitational Field
3.5 Continuous Versus Discontinuous Systems
3.6 General Evolution Criterion
4 Linear Non-equilibrium Thermodynamics
4.1 Discontinuous Systems
4.1.1 What is the Linear Non-equilibrium Thermodynamics
4.1.2 Onsager's Symmetry
4.1.3 Rayleigh's Dissipation Function
4.1.4 Minimum Entropy Production in Discontinuous Systems
4.1.5 The Least Dissipation Principle
4.1.6 The Balance of Entropy in a Copper Wire
4.1.7 Wiedemann-Franz' Law
4.1.8 Seebeck Effect
4.1.9 Peltier Effect
4.1.10 Thomson Effect
4.1.11 Kelvin's Thermocouple Equations
4.1.12 Knudsen Versus Pascal
4.2 Entropy Balance in Fluids
4.2.1 Dissipationless Fluids
4.2.2 Viscous Fluids
4.2.3 Joule-Thomson Throttled Expansion
4.2.4 Fluids with Electromagnetic Fields
4.2.5 Fluids with Many Non-reacting Species
4.2.6 Fluids with Many Species Reacting with Each Other
4.2.7 Fluids with Gravity
4.2.8 Local form of the Entropy Balance
4.2.9 Global form of the Entropy Balance: Back to the Copper Wire
4.3 Continuous Systems
4.3.1 A Slight Abuse of Notation
4.3.2 Thermodynamic Forces and Fluxes in Continuous Systems
4.3.3 Entropy Production Due to Diffusion
4.3.4 Saxen's Laws
4.3.5 Fick's Law
4.3.6 Soret Effect and Dufour Effect
4.3.7 Entropy Production Due to Reactions Among Species
4.3.8 Coupling of Diffusion and Reactions
4.3.9 Stability Versus the Coupling of Diffusion and Reactions
4.3.10 Minimum Entropy Production in Continuous Systems
5 Beyond Linear Non-equilibrium Thermodynamics
5.1 Gage et al.'s Theorem
5.2 Heat Conduction
5.2.1 Fourier's Law
5.2.2 Stability Versus Fourier's Law
5.3 Minimum Entropy Production
5.3.1 Joule Heating: Kirchhoff's Principle
5.3.2 Electric Arc
5.3.3 A Tale of Two Resistors
5.3.4 Back to Ohm
5.3.5 An Auxiliary Relationship
5.3.6 What if Joule Heating is Negligible?
5.3.7 Viscosity: Korteweg–Helmholtz' Principle
5.3.8 Maximum Economy: Yardangs, Rivers and the Human Blood
5.3.9 Porous Media
5.3.10 Stability Versus Kirchhoff's and Korteweg–Helmholtz' Principles
5.3.11 Convection at Moderate ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper R a) /StPNE pdfmark [/StBMC pdfmark Ra ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
5.3.12 Turbulent Flow Between Fixed Parallel Surfaces
5.4 Bejan's `Constructal Law'
5.5 Zipf's Principle of Least Effort
5.5.1 Of Words and Bells
5.5.2 City Air Makes You Free
5.5.3 Pareto
5.5.4 A Tale of Two Cities
5.5.5 Travels with Entropy
5.6 Maximum Entropy Production
5.6.1 Muffled Intuitions
5.6.2 Maximum Versus Minimum
5.6.3 A Thought Experiment
5.6.4 Again, the Copper Wire
5.6.5 Two Remarkable Exceptions
5.6.6 Heat Conduction in Gases
5.6.7 Convection at Large ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper R a) /StPNE pdfmark [/StBMC pdfmark Ra ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
5.6.8 The H-Mode
5.6.9 Shock Waves
5.6.10 Dunes
5.6.11 Detonation Versus Shock Waves
5.6.12 Solids
5.6.13 Earth's Oceans and Atmosphere
5.7 Lotka and Odum's Maximum Power Principle
5.8 Oscillating Relaxed States
5.8.1 Rules of Selection
5.8.2 Biwa et al.'s Experiment
5.8.3 Meija et al.'s Experiment
5.8.4 Hong et al.'s Experiment
5.8.5 Flame Quenching
5.8.6 Holyst et al.'s Simulations
5.8.7 Rauschenbach's Hypothesis
5.8.8 Rayleigh's Criterion of Thermoacoustics
5.8.9 Rijke's Tube
5.8.10 Sondhauss' Tube
5.8.11 Welander's Loop
5.8.12 Eddington and the Cepheids
6 A Room, a Heater and a Window
6.1 When Principles Collide
6.1.1 The Problem
6.1.2 Insufficient Approaches
6.1.3 Excess Entropy Production and Dissipative Structures
6.1.4 Selective Decay
6.1.5 Maximal Entropy
6.1.6 Extended Irreversible Thermodynamics
6.1.7 Steepest Ascent
6.1.8 Second Entropy
6.1.9 Information Thermodynamics and MaxEnt
6.1.10 Orthogonality Principle
6.1.11 Quasi-Thermodynamic Approach
6.1.12 Gouy-Stodola's Theorem and Entropy Generation
6.1.13 Much Ado for Nothing?
6.2 One Principle to Bind Them All?
6.2.1 A 1st Necessary Condition for Stability
6.2.2 Convection at Moderate ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper R a) /StPNE pdfmark [/StBMC pdfmarkRaps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark, Retrieved
6.2.3 Detonation Waves, Retrieved
6.2.4 Two Applications of Bejan's Constructal Law
6.2.5 Kohler's Principle
6.2.6 Entropy Production in a Radiation Field
6.2.7 Uniform Temperature: A Reciprocal Problem,...
6.2.8 ...Joule Heating,...
6.2.9 ...Viscous Heating,...
6.2.10 ... And Porous Media
6.2.11 A 2nd Necessary Condition for Stability
6.2.12 Entropy Production of a Radiating Body
6.2.13 No Heater, Two Windows
6.2.14 Resistors, Again
6.2.15 A 2nd Necessary Condition for Stability—General Form
6.2.16 Heat Conduction in Gases, Retrieved
6.2.17 Shock Waves and Dunes, Again
6.2.18 Back to Entropy Generation
6.2.19 Convection, Again
6.2.20 Crystal Growth, Retrieved
6.2.21 Liesegang and Gelation
7 The Garden of Forking Paths
Appendix
A.1 Proof of the General Evolution Criterion
A. 2 Euler-Lagrange Equations
A. 3 Lagrange Multipliers
A. 4 Proof of Gage et al.'s Theorem
Index
