The Universal Effectiveness of Topological Thermodynamics..Vol 6 Non-Equilibrium Systems and Irreversible Processes.

Use Preview to see a Table of Contents Vol6. The Cartan Topology of exterior differential forms is equivalent to the disconnected, non metrizable, Kolmogorov T0 poset (3) topology of four ingredients. Examples are given to demonstrate that non-equilibrium systems of distinguishable particles and irreversible processes are due to the non-metrizable features of the Kolmogorov-Cartan T0 topology. The problem of incorporating indistinguishable objects (statistical wave-diffusion distributions)into a topological perspective of Thermodynamics is accomplished by using differential form densities and Not-T0 topologies, without separation axioms. Homotopic processes on the differential form densities describe complex diffusion equations, such as the wave equation, the diffusion equation, the Landau-Ginsburg equations, the Schroedinger equation, and many others.