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
Unique-IP document downloads: 465 times
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.