Energy and particle number fluctuations in superconducting heterostructures

We consider fluctuations of the energy on a mesoscopic island coupled to two leads. We use the Keldysh effective action formalism to derive the Langevin equation for the energy of the island in a very general setting and show how the Langevin equation for the case of uncorrelated tunneling events is derived from a more general one. As an application of the theory, we consider a superconducting island coupled to two normal metal leads and calculate the statistics of the temperature (in the quasiequilibrium case) and the number of quasiparticle excitations on the island.