Control and Dissipation in Oscillatory Chemical Engines

Abstract

A simple model system for oscillatory reactions, which includes reverse reactions, is analyzed with respect to the control features that it develops far from equilibrium, and with respect to dissipation (entropy production), that is the efficiency of the reaction, from the point of view of chemical energy conversion. The study leads to the following observations which are likely to be independent of the model. The introduction of reverse reactions greatly enriches the types of behavior that the system displays, including hysteresis and excitability. The occurrence of oscillations is linked to a high differential susceptibility of the steady-state flux with respect to changes in overall affinity. Such control features are costly in terms of increased dissipation, but there is a possibility for limit cycle oscillations to reduce the average dissipation with respect to the steady-state values. When the system is subjected to imposed oscillations of moderate amplitude on the input side, we find a characteristic pattern in the dissipation spectrum: The dissipation in the autocatalytic reaction step of the mechanism is substantially lowered in the entrainment bands except near the boundaries between periodic and quasi-periodic behavior. However, the dissipation of the overall reaction is hardly affected because the output reaction cancels any advantages gained. If both the input and output sides are made to oscillate, then appreciable changes in the dissipation of the total reaction can be obtained. The sign of the change depends on the relative phase between input and output oscillations; small phase changes may lead to large changes in dissipation, which may be used as an additional control feature. A phase change can also alter the mode of operation from periodic to quasiperiodic with attendant changes in dissipation.