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We consider a stochastic model described by two stochastic differentialequations of motion; one is for the stochastic evolution forward in time andthe other for backward in time. We further introduce averaged quantities forthe two processes and construct the extended thermodynamic relation followingthe strategy of Sekimoto. By using this relation, we derive the fluctuationtheorems such as the Seifert relation, the Jarzynski relation and theKomatsu-Nakagawa non-equilibrium steady state with respect to the introducedaveraged quantities.

Extended Thermodynamic Relation and Fluctuation Theorem in Stochastic Dynamics with Time Reversed Process