An Introduction to Oscillatory Reactions

Many chemical and biochemical reactions can be in an oscillatory regime in which the concentrations of intermediates and products vary in a regular oscillatory way in time the oscillations may be sinusoidal but usually are not. Sustained oscillations require an open system with a continuous influx of reactants in a closed system oscillations may occur initially when the sjretem is far from equilibrium, but disappear as the system approaches equilibrium. A simple example of an oscillatory reaction is the Selkov model [1] 

If in such systems there is the possibility of more than one set of products, then the distributions into these several products may be effected by means of external periodic variations of constraints such as influx of reactants or temperature. For a review of earlier work of forced oscillations in systems of chemical interest see [4]. 

The dissipation, or the rate of entropy production, for chemical reactions 

Let us formulate the dissipation for a system with two internal variable X,Y) coupled to an input bath A and an output bath B. The internal reactant X is converted to the variable Y by an arbitrary non-linear reaction mechanism 

For the system-bath exchange we take first-order reactions 

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