  The convergence to equilibrium of mass action reaction-diffusion systems
arising from networks of chemical reactions is studied. The considered reaction
networks are assumed to satisfy the detailed balance condition and have no
boundary equilibria. We propose a general approach based on the so-called
entropy method, which is able to quantify with explicitly computable rates the
decay of an entropy functional in terms of an entropy entropy-dissipation
inequality based on the totality of the conservation laws of the system.
  As a consequence follows convergence to the unique detailed balance
equilibrium with explicitly computable convergence rates. The general approach
is further detailed for two important example systems: a single reversible
reaction involving an arbitrary number of chemical substances and a chain of
two reversible reactions arising from enzyme reactions.
