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We develop a method of calculating the full-counting statistics for anon-interacting fermionic system coupled to the memory-less reservoirs. Theevolution of the system is described by the Lindblad equation. By the basischange the Liouvillian operator is brought to the quadratic form. This allowsus a straightforward calculation of any observable in the non-equilibriumsteady state. We introduce the counting field in the Lindblad equation whichbrings us to the generating function and helps us to obtain all cumulants ofthe charge transport. For the two-site system we give the expression for thegenerating function. For system longer than two sites we perform numericalinvestigations which suggest that it in a uniform system the cumulants of order$k$ are independent of the size of the system for system sizes larger $k+1$.The counting statistics from the Lindblad approach does not take into accountinterference in the reservoirs which gives a decreased noise in comparison withthe Green function method which describes phase coherent leads. The currentobtained by two methods is the same, which relies on the current conservation.The Fano factors are different (with a linear relation connecting them) andallow to distinguish between memory-less and phase coherent reservoirs.

Lindblad equation for a non-interacting fermionic system: full-counting statistics