Complementary variational principles for lattice thermal conductivity

A method of complementary variational principles for the lattice thermal conductivity is presented. This two sided variational method gives sequences of upper and lower bounds on the exact thermal conductivity coefficient. The sequence of lower bounds can be recognised as the one presented by Benin. The sequence of upper bounds is a subsequence of an infinite sequence, with only odd number of terms present. One finds that the method of complementary variational principles is a very successful method of estimating the exact coefficient: it gives a controlled means of putting the estimated results into a band of desired accuracy around the exact transport coefficient.