Table of Contents:
Chapter 1: Introduction to Network Thermodynamics
What Is Network Thermodynamics?
Electronic Network Theory
Complex Systems Theory and the Characteristics of Modern Biology.
The Modeling Relation and Rosen's Distinction
The Explicit Recognition of Topological Contributions to System's Behavior
Physical Systems Theory
A Review of Classical Thermodynamics
Chapter 2: Equilibrium Thermodynamics:Review and Vocabulary
What Is "Thermodynamic" Reasoning?
Callen's First Postulate
The Extremum Principle and the Remainder of Callen's Postulates
The Chemical Potential as a Constitutive Rrelation
The Electrochemical Potential
Examples of the Use of the Chemical Potential to Calculate Relations for Constrained Equilibria
The Gibbs-Donnan Equilibrium Obeys the Nernst Equation as an Extremely Good Approximation
An aside: Application to Resting Cells
Chapter 3: Non-equilibrium Thermodynamics: From Onsager toPrigogine
The Nature of Stationary States away from Equilibrium (Steady States)
Entropy Production During an Irreversible Process and the Direction of Heat Flow
The Isothermal Dissipation Function
The Practical Phenomenological Equations
Chemical Reactions, Active Transport and Curie's Principle
Chapter 4: The Basic Ideas of Network Thermodynamics: I. The Constitutive Laws and Dynamic Systems
From Thermodynamics to Dynamic Systems: an Overview
Through and Across Variables
The Building Blocks: Constitutive Relations
Simple Independent Storage Events and the Generalization of Capacitance
Some Independent Inertial Processes
Chapter 5: The Basic Ideas of Network Thermodynamics: II. Graph Theoretical Methods for the Encoding of System Topology .
A Brief History of Graph Theory
Introduction to the Study of Networks and Graphs
An Example: The Network Approach to Some Rate Processes
Chapter 6: Network Thermodynamic Solutions to Steady State Linear Systems: Nodal and Mesh Analysis and Duality
The Systematic Approach to Networks
The Intimate Relation Between the Network's Topology and Kirchhoff's Laws
Nodal Analysis of a Network
The Generalized Dissipative Branch
Duality in Networks: Loop-Mesh Analysis is Equivalent to Node Analysis on the Dual
Dual Networks
Loop and Mesh Analysis
Chapter 7Dynamic Linear Systems and Cutsets: The Network Thermodynamic Generation of State Vector Equations
Time Dependent or "Dynamic" Linear Networks
Cut Set Analysis of Time Dependent Linear Networks
Cut Set Analysis: A Method Which Extends to Networks with Nonlinear Resistors, Capacitors and Inductors
Generalized Cut Set Analysis and the Analysis of RC Networks
State Vector Equations for Continuous-time Dynamic Networks
Nonlinear Dynamic Systems
The Use of the Proper Tree to Organize the Analysis
Using This Approach on Nonlinear Networks
Chapter 8: N-ports and Tellegen's Theorem: Energy Conversion, Degree of Coupling, Efficiency and Metrics . . . . . . .
Non-equilibrium Thermodynamics Provides the Phenomenological Description of N-ports
Network Thermodynamics Provides a Holistic View of the N-port
The Degree of Coupling and Efficiency of Energy Conversion in N-ports
The Degree of Coupling's Geometric Significance: the Metric and Its Demonstration of the Cannonical Nature of the Network Representation
The Phenomenological Approach
Phenomenology in Hierarchical Systems
Tellegen's Theorem and the Holistic View of Networks
Simplification of Computation in Linear Networks
Chapter 9: Applications of the N-port Concept: Topological Contributions to System Behavior, Multiport Current Dividers, and Other Innovations
Toward a Biological Circuit Theory
The Current Divider Principle in 1-port Networks
The Node-branch Incidence Matrix for the Current Divider
The Extension of the Current Divider Principle to N-ports
Mathematical Description of a Solute-volume Flow 2-port
Chapter 10: Making Nonlinearity Look Linear: The Reference State, Kinetics, and Non-equilibrium thermodynamics Get Married
The Relationship Between Kinetics and Onsager's Thermodynamics
Onsager's Triangle Reaction as a Network
Nonlinear Systems as Networks and the Reference State
The Need for Reference States: A Simple Kinetic Example
The Reference State
The Simple Carrier Model: Hill's Method of Analysis
Peusner's "Thermokinetic" Networks
The Creation of Peusner Networks for Thermokinetic Systems
The Principal of Detailed Balance: First Order vs. Pseudo-first Order Steps in the Network
The Choice of Reference State
An Example with Two Degrees of Freedom: Linear Description and Onsager Coefficients for a Given Reference State
Chapter 11: Simulation of Network Models Using SPICE: Making the Difficult Seem Easy
SPICE as a General Purpose Simulator
Using Resistors, Capacitors and Constant Sources
Some Examples
Controlled Sources, the "Magic" of SPICE
Chapter 12: Applications and Models: Compartmental Systems, Pharmacokinetics, Reaction Networks and Cancer Chemotherapy
Applications of Kinetics to Systems
The Compartmental Model of Frog Skin
The Energetics of Coupled Processes and Its Relationship to Compartmental Analysis
A Study of the Energetics of Sodium Transport in Frog Skin
Pharmacokinetic Models
Reaction Networks and Cancer Chemotherapy
Cardiovascular Models
Ecological Models
Structural Identifiability: What Network Thermodynamics Has to Offer
Appendix: A Short Review of Laplace Transforms
Chapter 13: Applications and Models: Epithelial Membranes in Kidney, Gut, and the Lingual Epithelium
The Epithelial Membrane Revisited
The Model of Coupled Solute/Volume Flow Across Loose Epithelia
The Tight Epithelium Model for Ion Transport and Electrophysiological Responses
Chapter 14: Epilogue: Towards a Theory of Complex Systems
Networks, Organization, Complexity and Life
Appendix: Some Topological Considerations in Thermodynamics: An Application of Network Thermodynamics
Onsager Reciprocity as a Topological Property
Reciprocity Defined as a Class of Simultaneous Properties
Reciprocity in Equilibrium Systems and the Existence of Potential Functions
Caratheodory's Proof and the Second Law of Thermodynamics
The Accessibility Theorem of Caratheodory
Proof of the Accessibility Theorem
Forms and the Exterior Calculus
Reciprocity in Classical Thermodynamics: Maxwell's Relations. . .
The Meaning of Receprocity in a Non-Equilibrium (Dynamic) System
The Topological Implications of Reciprocity