Information Contained in Open Systems by Example of Chemical Reaction Systems

Abstract

Abstract Spatially homogeneous chemical reaction systems with one or two intermediate reaction pro-ducts and with autocatalytic reactionsteps are considered. Because of their non-linearities, such open systems show already primitive forms of self-organization. In order to express the "information" contained in the structures occuring, a theory is developped for measuring that quantity by help of a fictive detector: In treating the stochastic reaction kinetics in the Fokker-Planck-equation approximation, expressions are derived for the averaged amount of information one gets by doing a measurement with the detector and for the temporal conservation of the message being detected. This concept is applied to a one-component reaction scheme that exhibits a non-equilibrium phase transition of second order resulting in bistability of the steady state. When pushing this reaction system from the near equilibrium side through its critical region to bi-stability, a certain amount of information becomes quasi conserved, thus giving rise to a definition of the degree of order of a self-organizating system. The problem of how the reaction system can be integrated into a greater chemical network as a "bit"-generator, is discussed. To explain what is necessary for the onset of a hard mode instability giving birth to limit-cycle behaviour, a two-component reaction scheme is constructed by superposing onto reaction steps causing conservative concentration oscillations those reactions of the former model system which are responsible for the instability occuring there. By applying the information formalism, again, a quasi-conservation of information is indicated, but with respect to a much smaller time scale. The consequences for using oscillating reaction models as an information pump within a network, and the necessity of a feed-back mechanism in order to get real information storage, are shortly mentioned. Finally, a one-component reaction scheme is outlined that shows successive phase transitions, each of these instabilities bringing out a higher degree of organization.