## The Non-Equilibrium Thermodynamic Environment and Prigogine's Dissipative Structures

**Authors:** R. M. Kiehn

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 ≠ 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, T, 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.

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 2 Aug 2008

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