Particle current fluctuations in a particle-nonconserving process

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.