Irreversible processes in Open non-equilibrium thermodynamic systems,
of topological dimension 4, can decay locally to Closed non-equilibrium
thermodynamic states, of topological dimension 3, by means of continuous topological
evolution. These topologically coherent, perhaps deformable, states of
one or more components appear to "emerge" as compact 3D Contact submanifolds,
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 a unique
extremal Hamiltonian process (as well as fluctuation 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 defect structures yield an evolutionary
behavior that can be associated with the idea of "stationary states"
far from equilibrium. If the fluctuation (spinor) components are weak, but not
zero, the emergent thermodynamic structure will ultimately 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 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 specific hardware devices,
but apply to all synergetic systems be they mechanical, biological, economical or political.
http://aux.planetphysics.org/files/books/137/Atme.pdf
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