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Adventures in Applied Topology..... Non-equilibrium systems are of Pfaff topological dimension > 2. Contact manifolds of Pfaff dimension 3 and Symplectic manifolds of Pfaff dimension 4 have complex vectorial components as eigendirection fields of the 2-form dA with zero quadratic form. They are Spinors, not classic vectors, and are the basis of topological fluctuations, dissipation, and irreveversibility.

Adventures in Applied Topology..... Continuous topological evolution can be used to encode non equilibrium thermodynamic systems and irreversible processes without the use of statistics or probability. Such methods are universal and apply to systems from the microscale to the cosmological scale. Thermodynamic irreversibility and the arrow of time are artifacts of topological change in four dimensions or more.

einstein alluded to the fact that thermodynamics is the most fundamental of the sciences. Yet classical thermodynamics has been more or less restricted to the study of idealistic equilibrium systems in terms of statistical methods. This book describes how a new perspective of continuous topological evolution can be used to describe the dynamics of Non-Equilibrium real world systems. Surprisingly, the topological methods are universal and apply to many diverse physical, chemical, biological and even economic and political systems. such systems consist of a multitude of different, topologically cherent, possibly self organizing, synergistic components, which extract energy from, and deliver waste to, their environments.

Adventures in Applied Topology..... Continuous topological evolution can be used to encode non equilibrium thermodynamic systems and irreversible processes without the use of statistics or probability. Such methods are universal and apply to systems from the microscale to the cosmological scale. Thermodynamic irreversibility and the arrow of time are artifacts of topological change in four dimensions or more. The second part of the book descibes a simple experiment (Falaco Solitons) that you can do in your swimming pool, emulating the ideas of Cosmic Strings. The third part models the universe in terms of the topological features of a Van der Waals gas near its critical point. The fourth part shows how the topological approach can explain the arrow of time in terms of irreversible thermodynamic processes.

A remarkable feature of Non-Equilibrium systems is their self organization, into long-lived topologically coherent structures or topological defects. A dramatic example of such a concept is given by the creation of Falaco Solitons in a swimming pool. The experiment is readily available to almost everyone, producing universal defect structures in a discontinuity surface. As topological structures, Falaco Solitons can occur at all scales, from the subatomic world of Quarks on a confinement thread to the Cosmological world of Branes attached by Strings, or even spiral galaxy pairs bound together with a Cosmic String. All visible in a swimming pool experiment!

Adventures in Applied Topology..... Continuous topological evolution can be used to encode non equilibrium thermodynamic systems and irreversible processes. Such methods are universal and apply to systems from the microscale to the cosmological scale. This volume uses topological techniques to describe persistent wakes and other topologically coherent but deformable strutures in fluids as thermodynamic states far from equilibrium and of Pfaff Topological dimension 3. The last part of the book is devoted to an explanation of Turbulence in terms of continuous, but irreversible, topological evolution in a domain of Pfaff Topological dimension 4, without the use of statistics.

 

Adventures in Applied Topology..... The methods of continuous topological evolution can be used to encode non equilibrium electromagnetic systems, such as a plasma, and to decide if certain processes applied to such systems are Thermodynamnically irreversible or not. The methods do not make use of statistics or probability theory. Several fundamental and new topological features (especially that of Topological Torsion and Topological Spin) of electromagnetic systems - which can be used to design new devices and processes - are introduced.