Non-Commutative Theory of Nonequilibrium Reveals Cantor Triadic Set in a Rich Ensemble of Coalescing Distributions

Authors: Jérôme Chauvet

Mathematics of non-commutative spaces is a rapidly growing research field, which has to date found convincing proof of its legitimacy in the nature, precisely, in quantum systems. In this paper, I evaluate the extension of fundamental non-commutativity to the theory of chemical equilibrium in reactions, of which little is known about its phenomenological implication. To do so, I assume time to be fundamentally discrete, with time values taken at integer multiples of a time quantum, or chronon. By integrating chemical ordinary differential equations (ODE) over the latter, two non-commutative maps are derived. The first map allows excluding some hypothetical link between chemical Poisson process and uncertainty due to non-commutativity, while the second map shows that, in first-order reversible schemes, orbits generate a rich collection of non-equilibrium statistics, some of which have their support close to the Cantor triadic set, a feature never reported for the Poisson process alone. This study points out the need for upgrading the current chemical reaction theory with noncommutativity-dependent properties.

Comments: 24 pages. Keywords: nonequilibrium, non-commutativity, chronon, Planck's time, Cantor set, Poisson process, coalescence, nuclear magnetic resonance

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Submission history

[v1] 13 Jan 2010
[v2] 23 Jan 2010
[v3] 28 Jan 2010

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