  We analytically calculate the cumulant generating function of energy and
particle transport in an open 1D Kitaev chain by utilizing the Keldysh
technique. The joint distribution of particle and energy currents obeys
different fluctuation relations in different regions of the parameter space as
a result of $U$(1) symmetry breaking and energy conservation. We discuss the
thermoelectricity of the Kitaev chain as a three terminal system and derive an
analytical expression of the maximum work power. The response theory up to the
second order is explicitly checked, and the result is consistent with the
relations derived from the fluctuation relation.
