  We consider a stochastic model described by two stochastic differential
equations of motion; one is for the stochastic evolution forward in time and
the other for backward in time. We further introduce averaged quantities for
the two processes and construct the extended thermodynamic relation following
the strategy of Sekimoto. By using this relation, we derive the fluctuation
theorems such as the Seifert relation, the Jarzynski relation and the
Komatsu-Nakagawa non-equilibrium steady state with respect to the introduced
averaged quantities.
