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