Statistics of temperature and potential fluctuations induced by coherent single particle sources

The prospect of time controlled information processing with individual electrons in nanoscale systems provides strong motivation for investigations of coupled charge and energy transport properties of single electron sources. Building on our recent work [F. Battista et al., Phys. Rev. Lett. 110, 126602 (2013)] we investigate theoretically the statistical properties of temperature and potential fluctuations in an electronic probe coupled to a generic single electron source. A detailed derivation of the cumulant generating function of the joint probability distribution is presented. Moreover, the probability distribution in stationary phase approximation is analysed.