Abstract

Most systems of interest in today's world are highly structured and highly interactive. They cannot be reduced to simple components without losing a great deal of their system identity. Network thermodynamics is a marriage of classical and non-equilibrium thermodynamics along with network theory and kinetics to provide a practical framework for handling these systems. The ultimate result of any network thermodynamic model is still a set of state vector equations. But these equations are built in a new informative way so that information about the organization of the system is identifiable in the structure of the equations. The domain of network thermodynamics is all of physical systems theory. By using the powerful circuit simulator, the Simulation Program with Integrated Circuit Emphasis ( ), as a general systems simulator, any highly non-linear stiff system can be simulated. Furthermore, the theoretical findings of network thermodynamics are important new contributions. The contribution of a metric structure to thermodynamics compliments and goes beyond other recent work in this area. The application of topological reasoning through Tellegen's theorem shows that a mathematical structure exists into which all physical systems can be represented canonically. The old results in non-equilibrium thermodynamics due to Onsager can be reinterpreted and extended using these new, more holistic concepts about systems. Some examples are given. These are but a few of the many applications of network thermodynamics that have been proven to extend our capacity for handling the highly interactive, non-linear systems that populate both biology and chemistry. The presentation is carried out in the context of the recent growth of the field of complexity science. In particular, the context used for this discussion derives from the work of the mathematical biologist, Robert Rosen.

Author Keywords: Network thermodynamics; Relational systems; Complexity theory

Article Outline

1. Introduction: why network thermodynamics?

1.1. Thermodynamics is the study of energy transformation properties common to all systems

1.2. What is thermodynamic reasoning?

1.3. Relational systems theory and network thermodynamics: the role of topology

1.4. Network thermodynamics and chemistry

2. A short review of classical (equilibrium) thermodynamics

2.1. Postulate I

2.2. Postulate II

3. A brief review of non-equilibrium thermodynamics

3.1. The isothermal dissipation function

3.2. The phenomenological equations

3.3. The Onsager reciprocal relations

3.4. Minimum dissipation

4. The structure of network thermodynamics as a formalism

4.1. The network thermodynamic model of a system

4.1.1. The observable characterizing the networks using an abstraction of the network elements

4.1.2. Analog models

4.1.3. The constitutive laws for physical systems

4.1.3.1. The resistance as a general systems element

4.1.3.2. The capacitance as a general systems element

4.1.4. The topology of a network

4.1.4.1. The formal description of a network

4.1.4.2. The formal solution of a linear resistive network

5. The use of multiports for coupled processes: the entry to biological applications

5.1. Linear multiports are based on non-equilibrium thermodynamics

5.2. Non-linear multiports are simulated on the computer

6. Simulation of non-linear networks on

6.1. Simulation of chemical reaction networks

6.2. Simulation of mass transport in compartmental systems

6.3. Simulation of bulk flow

6.4. Non-linear multiports are constructed from controlled sources in

7. Thermostatic networks: equilibrium revisited

8. Network thermodynamics contributions to theory: some fundamentals

8.1. The canonical representation of linear non-equilibrium systems, the metric structure of thermodynamics and the energetic analysis of coupled systems

8.2. The Onsager reciprocal relations (ORR)

9. Relational networks and beyond

9.1. A message from network theory

9.2. Isotonic transport in epithelia as an emergent property of the 2-port current divider

10. The relationship of network thermodynamics to chemistry and biology: past, present and future

References