Network thermodynamics and complexity: a transition to relational systems theory

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 (SPICE), 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.