  According to the Green-Kubo theory of linear response, the conductivity of an
electronically gapped liquid can be expressed in terms of the time correlations
of the adiabatic charge flux, which is determined by the atomic velocities and
Born effective charges. We show that topological quantisation of adiabatic
charge transport and gauge invariance of transport coefficients allow one to
rigorously express the electrical conductivity of an insulating fluid in terms
of integer-valued, scalar, and time-independent atomic oxidation numbers,
instead of real-valued, tensor, and time-dependent Born charges.
