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

Microreversibility, fluctuation relations, and response properties in 1D Kitaev Chain