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We consider Piecewise Deterministic Markov Processes (PDMPs) with a finiteset of discrete states. In the regime of fast jumps between discrete states, weprove a law of large number and a large deviation principle. In the regime offast and slow jumps, we analyze a coarse-grained process associated to theoriginal one and prove its convergence to a new PDMP with effective forcefields and jump rates. In all the above cases, the continuous variables evolveslowly according to ODEs.  Finally, we discuss some applications related to the mechanochemical cycle ofmacromolecules, including strained--dependent power--stroke molecular motors.Our analysis covers the case of fully--coupled slow and fast motions.

Averaging and large deviation principles for fully-coupled piecewise deterministic Markov processes and applications to molecular motors