  We study the statistics of heat transferred in a given time interval $t_M$,
through a finite harmonic chain, called the center $(C)$, which is connected
with two heat baths, the left $(L)$ and the right $(R)$, that are maintained at
two different temperatures. The center atoms are driven by an external
time-dependent force. We calculate the cumulant generating function (CGF) for
the heat transferred out of the left lead, $Q_L$, based on two-time measurement
concept and using nonequilibrium Green's function (NEGF) method. The CGF can be
concisely expressed in terms of Green's functions of the center and an
argument-shifted self-energy of the lead. The expression of CGF is valid in
both transient and steady state regimes. We consider three different initial
conditions for the density operator and show numerically, for one-dimensional
(1D) linear chains, how transient behavior differs from each other but finally
approaches the same steady state, independent of the initial distributions. We
also derive the CGF for the joint probability distribution $P(Q_L,Q_R)$, and
discuss the correlations between $Q_L$ and $Q_R$. We calculate the total
entropy flow to the reservoirs. In the steady state we explicitly show that the
CGF obeys steady state fluctuation theorem (SSFT). Classical results are
obtained by taking $\hbar \to 0$. The method is also applied to the counting of
the electron number and electron energy, for which the associated self-energy
is obtained from the usual lead self-energy by multiplying a phase or shifting
the contour time, respectively.
