Intrinsic Non-Commutativity and Statistical Multiplicity in a Reversible Chemical Reaction

Abstract

Mathematics of non-commutative spaces is a growing research field, which has to date found convincing proof of legitimacy in nature, precisely, in quantum systems. In this paper, we 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, we 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 an hypothetical link between chemical Poisson process and uncertainty due to non-commutativity, while the second map shows that, in first-order reversible schemes, orbits deploy within a rich collection of non-equilibrium statistics, some of which have their support matching  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.