We provide a detailed investigation on the fluctuations of two currents in the discrete model of Feynman's ratchet proposed by Jarzynski and Mazonka in 1999. Two macroscopic currents are identified, with the corresponding affinities determined using Schnakenberg's graph analysis. We also compute full counting statistics of the two currents and show that a fluctuation theorem holds for their joint probability distribution. Moreover, fluctuation-dissipation relation, Onsager reciprocal relation and their nonlinear generalizations are numerically shown to be satisfied in this model.

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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.