The Non-Equilibrium Thermodynamic Environment and Prigogine’s Dissipative Structures

This essay is based on the fundmental assumption that any physical system of synergetic parts is a thermodynamic system. The universality of thermodynamics is due to the fact that thermodynamic homogeneous properties, such as pressure, temperature and their analogs, do not depend upon size or shape. That is, thermodynamics is a topological (not a geometrical) theory. By use of Cartan’s methods of exterior differential forms and their topological properties of closure, it is possible to define and construct examples for the universal concepts of: [1] Continuous Topological Evolution of topological properties which in effect is a dynamical version of the First Law. [2] Topological Torsion and Pfaff Topological Dimension which distinguishes equilibrium (PTD < 3, TT = 0) and non-equilibrium systems (PTD > 2, TT 6= 0). [3] A Topological Thermodynamic Environment of PTD = 4. [4] Thermodynamic irreversible processes, which cause self-similar evolution in the environment, and emergence of self-organized states of PTD = 3 as topological defects in the PTD = 4 environment. These results clarify and give credence to Prigogine’s conjectures about dissipative structures. [5] A universal thermodynamic phase function, Θ, which can have a singular cubic factor equivalent to a deformed, universal, van der Waals gas. This van der Waals gas admits negative pressure and dark matter properties, which are current themes in Astronomy and GR.