  We extend [Bru-de Siqueira Pedra-Hertling, J. Math. Phys. 56 (2015) 051901]
in order to study the linear response of free fermions on the lattice within a
(independently and identically distributed) random potential to a macroscopic
electric field that is time- and space-dependent. We obtain the notion of a
macroscopic AC-conductivity measure which only results from the second
principle of thermodynamics. The latter corresponds here to the positivity of
the heat production for cyclic processes on equilibrium states. Its Fourier
transform is a continuous bounded function which is naturally called
(macroscopic) conductivity. We additionally derive Green-Kubo relations
involving time-correlations of bosonic fields coming from current fluctuations
in the system. This is reminiscent of non-commutative central limit theorems.
