  The convergence to equilibrium for renormalised solutions to nonlinear
reaction-diffusion systems is studied. The considered reaction-diffusion
systems arise from chemical reaction networks with mass action kinetics and
satisfy the complex balanced condition. By applying the so-called entropy
method, we show that if the system does not have boundary equilibria, then any
renormalised solution converges exponentially to the complex balanced
equilibrium with a rate, which can be computed explicitly up to a finite
dimensional inequality. This inequality is proven via a contradiction argument
and thus not explicitly. An explicit method of proof, however, is provided for
a specific application modelling a reversible enzyme reaction by exploiting the
specific structure of the conservation laws.
  Our approach is also useful to study the trend to equilibrium for systems
possessing boundary equilibria. More precisely, to show the convergence to
equilibrium for systems with boundary equilibria, we establish a sufficient
condition in terms of a modified finite dimensional inequality along
trajectories of the system. By assuming this condition, which roughly means
that the system produces too much entropy to stay close to a boundary
equilibrium for infinite time, the entropy method shows exponential convergence
to equilibrium for renormalised solutions to complex balanced systems with
boundary equilibria.
