  The concept of continuous topological evolution, based upon Cartan's methods
of exterior differential systems, is used to develop a topological theory of
non-equilibrium thermodynamics, within which there exist processes that exhibit
continuous topological change and thermodynamic irreversibility. The technique
furnishes a universal, topological foundation for the partial differential
equations of hydrodynamics and electrodynamics; the technique does not depend
upon a metric, connection or a variational principle. Certain topological
classes of solutions to the Navier-Stokes equations are shown to be equivalent
to thermodynamically irreversible processes.
