Particles vs Waves: Finite Topological Thermodynamics
Robert M. Kiehn
Traditional physical theories have been constrained historically by assumptions of "geo-metrical" di?eomorphisms, invariant symmetries, and topological invariance. These ideas are useful to the understanding of equilibrium thermodynamic states, and processes that lead to time reversibility of equilibrium topological systems, and the conservation of energy. However, the geometrical constraints o?er no insight into non-equilibrium thermodynamic systems and irreversible processes, such as observed in the biological environment. Geometrical tensor methods are inadequate and must be replaced by topological thinking. Emphasis must be placed upon methods that describe continuous topological evolution, and not topological invariance. For example, to form a categorical marriage between gravity and quantum mechanics requires the recognition that the topological structure of "particles" is di?erent from the topological structure of "waves".
