  In the general process of eliminating dynamic variables in Markovian models,
there exists a difference in the irreversible entropy production between the
original and reduced dynamics. We call this difference the hidden entropy
production, since it is an invisible quantity when only the reduced system's
view is provided. We show that this hidden entropy production obeys a new
integral fluctuation theorem for the generic case where all variables are
time-reversal invariant, therefore supporting the intuition that entropy
production should decrease by coarse graining. It is found, however, that in
cases where the condition for our theorem does not hold, entropy production may
also increase due to the reduction. The extended multibaker map is investigated
as an example for this case.
