The fluctuation theorem for currents in semi-Markov processes

The fluctuation theorem for currents in semi-Markov processes satisfying the condition of direction–time independence is proved. The thermodynamic affinities as well as the corresponding fluctuating currents are defined using graph theory and the cyclic representation of the process. The fluctuation theorem is obtained by demonstrating a fundamental symmetry property for the evolution operator of the process. This fundamental symmetry of the evolution operator is also proved for the Markovian case. The results are illustrated with a semi-Markov process describing ion currents through a membrane