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Robert M. Kiehn
Category Theory of Topological Thermodynamics

Date: 2011-11-05 Time: 07:00 - 09:00 US/Pacific (1 decade 2 years ago)
America/Los Angeles: 2011-11-05 07:00 (DST)
America/New York: 2011-11-05 10:00 (DST)
America/Sao Paulo: 2011-11-05 11:00
Europe/London: 2011-11-05 14:00
Asia/Colombo: 2011-11-05 19:30
Australia/Sydney: 2011-11-06 01:00 (DST)

Where: Online Video Conference
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Classical thermodynamics consists of equilibrium geometric configuration spaces which are subjected to various reversible evolutionary processes based upon the geometric covariant differential. In this article these ideas will be extended to the more general category theory of topological thermodynamics. The theory includes coexistent equilibrium and non-equilibrium topological spaces. The different topological spaces encode thermodynamic states of topologically distinguishable elements (countable particles or properties) as well as thermodynamic states of topologically indistinguishable elements (statistical ensembles of complex diffusion-wavelets). The morphisms of the category are dynamical concepts that use E. Cartan's "magic" formula (based on the Lie differential, not the covariant derivative) to describe continuous topological evolution of the various topological states, whose elements are constructed in terms exterior differential forms. The result is a theory of Thermodynamics that has universal application to all synergistic non-deterministic and deterministic systems. The methods have been applied to irreversible dissipative processes in plasmas, turbulent fluids, chaotic dynamics, self similarity, solitons, and emergence of topological defects. The theory justifies by example Prigogene's conjecture of the emergence of states (topological defects) far from equilibrium. The theoretical result that the phase velocity of light can have 4 different speeds of propagation (two faster and two less than c) in rotating media that has both constitutive properties of optical activity and Faraday rotation is justified by experiments as measured by dual polarized Sagnac ring lasers. The methods open the way to a thermodynamic understanding of the life and death of economic systems, political systems, biological systems, and Quantum Systems. The Wave-Particle dualism can be explained in terms of non equilibrium thermodynamic states far from equilibrium with indistinguishable elements (waves) coexisting with thermodynamic states of distinguishable elements (particles) that are defined by rational fraction deRham period integrals.