The electronic distribution in devices with sufficiently small dimensions may not be in thermal equilibrium with their surroundings. Systems where the occupancies of electronic states are solely determined by tunneling processes are analyzed. It is shown that the effective temperature of the device may be higher, or lower, than that of its environment, depending on the applied voltage and the energy dependence of the tunneling rates. The I-V characteristics become asymmetric. Comparison with recent experiments is made. 75.10.Jm, 75.10.Lp, 75.30.Ds. In small devices, the coupling between electrons and the lattice is suppressed. At sufficiently low temperatures, only long wavelength accoustical phonons are excited. If the electrons are localized in a region much smaller than the wavelength of the phonons, the interaction between the electrons and the phonons is significantly reduced [1]. As a result, the electron temperature may be different from that of the surrounding medium.Usually, the electron temperature in small devices tend to be higher than that of the environment, because of dissipation at the device [1] (see also [2]), via shake-up processes. This effect can explain a number of experiments [3,4].In the following, we analyze the electronic distribution in a small device, when it is controlled by the electronic exchange with the external leads. The general equations which describe the single level occupancies were first discussed in [6,5]. These authors considered mostly the inluence of a non negligible single level spacing in the I-V characteristics of semiconductor nanostructures. In these systems, the effects of the energy dependence of the transmission through the barrier, or of the density of states in the external leads is not important. We will generalize the previous work to situations where energy dependent tunneling rates also contribute to modify the electronic distribution. As it will be seen below, an energy dependent tunneling rate, T (ǫ), can modify significantly the electronic distribution in the central electrode of a single electron device, if T ′ (ǫ)/T (ǫ) is comparable to the inverse of the temperature at which the device is operated. Such a situation can be realized when an electrode has a strongly dependent density of states, or if the tunneling process takes place close to the top of a barrier. The first case is relevant to the experiments reported in [7], where one of the electrodes is made of graphite, and to the experiments presented in [8], where the electrodes are made of superconducting Al, and tunneling processes take place near the gap edges. Asymmetric I-V characteristics have also been reported in [10]. Some features of these experiments are also consistent with the work reported here.A particularly interesting case is presented in [7]. The observed Coulomb staircase can only be fitted by the orthodox theory [11][12][13], if an effective temperature of ∼ 170K is assumed, although the experiment is performed at room temperature. A large temperature difference between the...