A new statistical model for the combined effects of decoherence, energy redistribution and dissipation on electron transport in large quantum systems is introduced. The essential idea is to consider the electron phase information to be lost only at randomly chosen regions with an average distance corresponding to the decoherence length. In these regions the electronʼs energy can be unchanged or redistributed within the electron system or dissipated to a heat bath. The different types of scattering and the decoherence leave distinct fingerprints in the energy distribution functions. They can be interpreted as a mixture of unthermalized and thermalized electrons. In the case of weak decoherence, the fraction of thermalized electrons show electrical and thermal contact resistances. In the regime of incoherent transport the proposed model is equivalent to a Boltzmann equation. The model is applied to experiments with carbon nanotubes. The excellent agreement of the model with the experimental data allows to determine the scattering lengths of the system.