  We propose a model that describes cyclic state transitions of a micromachine
driven by a catalytic chemical reaction. We consider a mechano-chemical
coupling of variables representing the degree of a chemical reaction and the
internal state of a micromachine. The total free energy consists of a tilted
periodic potential and a mechano-chemical coupling energy. We assume that the
reaction variable obeys a deterministic stepwise dynamics characterized by two
typical time scales, i.e., the mean first passage time and the mean first
transition path time. To estimate the functionality of a micromachine, we focus
on the quantity called "nonreciprocality" and further discuss its dependence on
the properties of catalytic reaction. For example, we show that the
nonreciprocality is proportional to the square of the mean first transition
path time. The explicit calculation of the two time scales within the
decoupling approximation model reveals that the nonreciprocality is inversely
proportional to the square of the energy barrier of catalytic reaction.
