Prigogine’s Thermodynamic Emergence and Continuous Topological Evolution

Irreversible processes can be described in Open non-equilibrium thermodynamic systems, of topological dimension 4. By means of Continuous Topological evolution, such processes can cause local decay to Closed non-equilibrium thermodynamic states, of topological dimension 3. These topologically coherent, perhaps deformable, regions or states of one or more components appear to "emerge" as compact 3D Contact submanifolds that can be defined as topological defects in the 4D Symplectic manifold. These emergent states are still far from equilibrium, as their topological (not geometrical) dimension is greater than 2. The 3D Contact submanifold admits evolutionary processes with a unique extremal Hamiltonian vector component, as well as fluctuation spinor components. If the subsequent evolution is dominated by the Hamiltonian component, the emergent topological defects will maintain a relatively long-lived, topologically coherent, approximately non-dissipative structure. These topologically coherent, "stationary states" far from equilibrium ultimately will decay, but only after a substantial "lifetime". Analytic solutions and examples of these processes of Continuous Topological Evolution give credence, and a deeper understanding, to the general theory of self-organized states far from equilibrium, as conjectured by I. Prigogine. Moreover, in an applied sense, universal engineering design criteria can be developed to minimize irreversible dissipation and to improve system efficiency in general non-equilibrium situations. As the methods are based on universal topological, not geometrical, ideas, the general thermodynamic results apply to all synergetic topological systems. It may come as a surprise, but ecological applications of thermodynamics need not be limited to the design of specific hardware devices, but apply to all synergetic systems, be they mechanical, biological, economical or political. 1 THE POINT OF DEPARTURE 1.1 Topological Evolution vs. Geometrical Evolution This essay represents a brief summary of the features of a topological theory of thermodynamics. The point of departure starts with a topological (not statistical) formulation of dynamics, which can furnish a universal foundation for the Partial Differential Equations of non-equilibrium