  The Hamiltonian of mean force is a widely used concept to describe the
modification of the usual canonical Gibbs state for a quantum system whose
coupling strength with the thermal bath is non-negligible. Here we
perturbatively derive general approximate expressions for the Hamiltonians of
mean force in the weak-coupling approximation and in the high-temperature one.
We numerically analyse the accuracy of the corresponding expressions and show
that the precision of the Bloch-Redfield equantum master equation can be
improved if we replace the original system Hamiltonian by the Hamiltonian of
mean force.
