Network thermodynamics and complexity: a transition to relational systems theory.

Area of Science:

• Physical Systems Theory
• Complexity Science
• Non-equilibrium Thermodynamics

Background:

• Modern systems are highly structured and interactive, losing identity when reduced to simple components.
• Existing thermodynamic frameworks struggle to capture the holistic nature of complex systems.

Purpose of the Study:

• To present network thermodynamics as a unified framework for analyzing complex, interactive systems.
• To demonstrate how network thermodynamics integrates classical and non-equilibrium thermodynamics with network theory.
• To highlight the application of network thermodynamics in simulating and understanding biological and chemical systems.

Main Methods:

• Developed a network thermodynamic modeling approach.
• Utilized the Simulation Program with Integrated Circuit Emphasis (SPICE) for simulating non-linear systems.
• Applied topological reasoning, including Tellegen's theorem, for canonical system representation.
• Reinterpreted and extended Onsager's results in non-equilibrium thermodynamics.

Main Results:

• Network thermodynamic models yield state vector equations that explicitly represent system organization.
• SPICE enables simulation of highly non-linear and stiff systems.
• Metric structures and topological reasoning provide novel thermodynamic insights.
• The framework extends the capacity for analyzing complex biological and chemical systems.

Conclusions:

• Network thermodynamics offers a powerful, holistic approach to physical systems theory.
• This framework complements and extends existing work in thermodynamics and complexity science.
• The approach provides a canonical representation for all physical systems, enhancing analytical capabilities.