  We propose a general framework of the geometric-phase interpretation for
counting statistics. Counting statistics is a scheme to count the number of
specific transitions in a stochastic process. The cumulant generating function
for the counting statistics can be interpreted as a `phase', and it is
generally divided into two parts: the dynamical phase and a remaining one. It
has already been shown that for cyclic evolution the remaining phase
corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan
phase. We here show that the remaining phase also has an interpretation as a
geometric phase even in noncyclic and nonadiabatic evolution.
