  Matsubara dynamics has recently emerged as the most general form of a
quantum-Boltzmann-conserving classical dynamics theory for the calculation of
single-time correlation functions. Here, we present a generalization of
Matsubara dynamics for the evaluation of multi-time correlation functions. We
show that the Matsubara approximation can also be used to approximate the
two-time symmetrized double Kubo transformed correlation function. By a
straightforward extension of these ideas to the multi-time realm, a multi-time
Matsubara dynamics approximation can be obtained for the multi-time fully
symmetrized Kubo transformed correlation function. Although not a practical
method, due to the presence of a phase-term, this multi-time formulation of
Matsubara dynamics represents a benchmark theory for future development of
Boltzmann preserving semi-classical approximations to general higher order
multi-time correlation functions.
