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We obtain the large deviation function for entropy production of the mediumand its distribution function for two-site totally asymmetric simple exclusionprocess(TASEP) and three-state unicyclic network. Since such systems aredescribed through microscopic irreversible transitions, we obtaintime-dependent transition rates by sampling the states of these systems at aregular short time interval $\tau$. These transition rates are used to derivethe large deviation function for the entropy production in the nonequilibriumsteady state and its asymptotic distribution function. The shapes of the largedeviation function and the distribution function depend on the value of themean entropy production rate which has a non-trivial dependence on the particleinjection and withdrawal rates in case of TASEP. Further, it is argued that incase of a TASEP, the distribution function tends to be like a Poissondistribution for smaller values of particle injection and withdrawal rates.

Entropy production and large deviation function for systems with microscopically irreversible transitions