self-consistent reservoirs are typically (in the sense of RMT) governed by Ohm and Fourier laws.

General Properties {#General properties}
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In this section, we consider that the system is coupled to $N+2$ terminals (we use $\L$ and $\R$ to be consistent with the next sections) and suppose that its transport properties are given in terms of some scattering matrix $S$ (see  \[The General System\]).

In the linear response regime and under the assumption that the scattering matrix $S$ does not depend on the energy, we will determine the general transport properties of the system. All these properties are expected to hold on physical grounds and actually some of them have recently been obtained in full generality [@CA]. Nevertheless, in this paper, we are only interested in some particular situations in which the derivations of these properties are somehow simpler.

Linear Transport Analysis {#Linear transport analysis}
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In the remainder of this paper we shall always rely on the following.

We assume that, for $i \in \{\L, \R, 1, \dots,
N\}$, $$\begin{aligned}
T_i &=& T + \delta T_i~,\\
\mu_i &=& \mu + \delta \mu_i~,\end{aligned}$$ where $T > 0$ and $\mu \in \mathbb{R}$ are some reference values, while $\delta T_i \in \mathbb{R}$ 