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We investigate the full-counting statistics (FCS) of energy transport carriedby electrons in molecular junctions for the Anderson-Holstein model in thepolaronic regime. Using two-time quantum measurement scheme, generatingfunction (GF) for the energy transport is derived and expressed as a Fredholmdeterminant in terms of Keldysh nonequilibrium Green's function in the timedomain. Dressed tunneling approximation is used in decoupling the phonon cloudoperator in the polaronic regime. This formalism enables us to analyze the timeevolution of energy transport dynamics after a sudden switch-on of the couplingbetween the dot and the leads towards the stationary state. The steady stateenergy current cumulant GF in the long time limit is obtained in the energydomain as well. Universal relations for steady state energy current FCS arederived under finite temperature gradient with zero bias and this enables us toexpress the equilibrium energy current cumulant by a linear combination oflower order cumulants. Behaviors of energy current cumulants in steady stateunder temperature gradient and external bias are numerically studied andexplained. Transient dynamics of energy current cumulants is numericallycalculated and analyzed. The universal scaling of normalized transient energycumulants is found under both temperature gradient and external bias.

Full-counting statistics of energy transport of molecular junctions in the polaronic regime