By Hitchcock F.L.

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Topological change can occur continuously or discontinuously. The focus in this monograph is on continuous topological change, and as will be demonstrated below, topological change is a necessary requirement for thermodynamic irreversibility [192]. 2 Absolute Integral Invariants There are two types of invariant integrals, Absolute and Relative integral invariants. If the exterior p-form that forms the integrand is exact, the Absolute integral invariant places conditions only on the boundary of the domain of integration.

17. On spaces of Pfaff topological dimension 4, the Cayley-Hamilton theorem produces a characteristic polynomial with similarity invariant coefficients which will generate the format of the Gibbs function for a (universal) van der Waals gas, with a well defined critical point and binodal and spinodal lines. The same technique can be applied to dynamical systems. The combined thermodynamic-topological perspective presented in this monograph uses the mathematical tools of exterior differential forms to describe the topological features of physical systems, and vector fields to describe the continuous evolutionary processes that may or may not change the topology of the physical system.

Note that these topological specifications as given above are determined entirely from the functional properties of the physical system encoded as a 1-form of Action, A. The system topological categories do not involve a process, which is encoded (to within a factor) by some vector direction field, V4 .

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