  Based on two-time observation protocol, we consider heat transfer in a given
time interval $t_{M}$ in lead-junction-lead system taking coupling between the
leads into account. In view of the two-time observation, consistency conditions
are carefully verified in our specific family of quantum histories.
Furthermore, its implication is briefly explored. Then using nonequilibrium
Green's function (NEGF) method, we obtain an exact formula for the cumulant
generating function for heat transfer between the two leads valid in both
transient and steady-state regimes. Also, a compact formula for the cumulant
generating function in the long-time limit is derived, for which the
Gallavotti-Cohen (GC) fluctuation symmetry is explicitly verified. In addition,
a brief discussion of Di Ventra's trick regarding whether the effect of the
repartitioning procedure of the total Hamiltonian on nonequilibium steady-state
current fluctuation exists is given. All kinds of properties of nonequilibrium
current fluctuations such as the fluctuation theorem in different time regimes
could be readily given according to these exact formulas.
