  Dynamical fluctuations in classical adiabatic processes are not considered by
the conventional classical adiabatic theorem. In this work a general result is
derived to describe the intrinsic dynamical fluctuations in classical adiabatic
processes. Interesting implications of our general result are discussed via two
subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model
with an adiabatically moving fixed-point solution, and the possible "pollution"
to Hannay's angle or to other adiabatic phase objects for adiabatic processes
involving non-fixed-point solutions.
