heat transport, one expresses the (average) electric and heat currents through a conductor in terms of the scattering data of this conductor. Therefore, starting from the EY-model, we shall make the following crucial modifications:

-   The main modification concerns the scattering version of the disc. There are two features of the EY-model that should be pointed out: (i) The exact position of the disc within a given cell is not important, so one may consider the cell represented in  \[The two Systems\] (left). (ii) Once the system has reached a stationary state satisfying LTE, the boxes containing the discs are at equilibrium and consequently the net (average) particle and energy currents into these boxes vanish [@Wagner; @KlagesPRL; @Rateitschak].

    Therefore, in the scattering approach, one can obtain an *effective* description of the discs as follows[^1]: We replace the boxes containing the discs by independent particle reservoirs with characteristic temperatures and chemical potentials such that the net (average) electric and heat currents into these particle reservoirs vanish ( \[The two Systems\] and \[The Quantum System\]). In this manner, the particles in a given cell will be in equilibrium with their respective reservoir, the system will be in local thermal equilibrium.

    Although the 