  We have considered a one-dimensional coagulation-decoagulation system of
classical particles on a finite lattice with reflecting boundaries. It is known
that the system undergoes a phase transition from a high-density to a
low-density phase. Using a matrix product approach we have obtained an exact
expression for the average entropy production rate of the system in the
thermodynamic limit. We have also performed a large deviation analysis for
fluctuations of entropy production rate and particle current. It turns out that
the characteristics of the kink in the large deviation function can be used to
spot the phase transition point. We have found that for very weak driving field
(when the system approaches to its equilibrium) and also for very strong
driving field (when the system is in the low-density phase) the large deviation
function for fluctuations of entropy production rate is almost parabolic while
in the high-density phase it prominently deviates from Gaussian behavior. The
validity of the Gallavotti-Cohen fluctuation relation for the large deviation
function for particle current is also verified.
