and the self-consistent reservoirs are sufficiently small, then one may interpret the self-consistent reservoirs as ideal potentiometers and thermometers [@Engquist; @Sivan-Imry].

-   The transport properties of the cells will be given in terms of $N$ scattering matrices $S^{(1)},\dots
      ,S^{(N)}$. However, we will work mostly in terms of the scattering matrix $S$ associated to the global multi-terminal system, which is obtained by composing the $N$ local scattering matrices together.

-   In order to have some generality, we will describe the particle reservoirs in terms of the three standard physical distributions: the classical Maxwell-Boltzmann distribution and the quantum Fermi-Dirac and Bose-Einstein distributions. We assume that the particles may carry some charge $e$, so that we may speak of electric currents instead of particle currents. Nevertheless, we shall assume, as in the EY-model, that the particles do not interact with each other.

For obvious reasons, we now call the cells [*quantum dots*]{}. In the EY-model, the outer boundaries of the cells were chosen such that the system was chaotic. We shall at some point impose this property by assuming that the quantum dots are classically chaotic.

The organisation of this paper is as follows. In  \[The model\], we establish the framework of multi-terminal 