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!
