  In this work we investigate the convergence to equilibrium for mass action
reaction-diffusion systems which model irreversible enzyme reactions. Using the
standard entropy method in this situation is not feasible as the
irreversibility of the system implies that the concentrations of the substrate
and the complex decay to zero. The key idea we utilise in this work to
circumvent this issue is to introduce a family of cut-off partial entropy
functions which, when combined with the dissipation of a mass like term of the
substrate and the complex, yield an explicit exponential convergence to
equilibrium. This method is also applicable in the case where the enzyme and
complex molecules do not diffuse, corresponding to chemically relevant
situation where these molecules are large in size.
