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We consider an irreducible continuous time Markov chain on a finite statespace and with time periodic jump rates and prove the joint large deviationprinciple for the empirical measure and flow and the joint large deviationprinciple for the empirical measure and current. By contraction we get thelarge deviation principle of three types of entropy production flow. We derivesome Gallavotti-Cohen duality relations and discuss some applications.

Level 2.5 large deviations for continuous time Markov chains with time periodic rates