  The thermal conductivity of a dense {\it multi-component} plasma is critical
to the modeling of accreting neutron stars. To this end, we perform large-scale
molecular dynamics simulations to calculate the static structure factor of the
dense multi-component plasma in the neutron star crust from near the
photosphere-ocean boundary to the vicinity of the neutron drip point. The
structure factors are used to validate a microscopic linear mixing rule that is
valid for arbitrarily complex plasmas over a wide range of Coulomb couplings.
The microscopic mixing rule in turn implies and validates the linear mixing
rule for the equation of state properties and also the linear mixing rule for
the electrical and thermal conductivities of dense multi-component plasmas. To
make our result as useful as possible, for the specific cases of electrical and
thermal conductivities, we provide a simple analytic fit that is valid for
arbitrarily complex multi-component plasmas over a wide range of Coulomb
couplings. We compute the thermal conductivity for a representative
compositional profile of the outer crust of an accreting neutron star in which
hundreds of nuclear species can be present. We utilize our results to
re-examine the so-called impurity parameter formalism as used to characterize
impure plasmas.
