A new method  is introduced to estimate transport coefficients in extended systems from optimally short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and the cepstral analysis of time series. Information from the full sample power spectrum of the relevant current for a single trajectory is leveraged to evaluate and optimally reduce the noise affecting its zero-frequency value, whose expectation is proportional to the corresponding transport coefficient. Our method is unbiased and consistent, in that both the resulting bias and statistical error can be made arbitrarily small in the long-time limit. A simple protocol to evaluate thermal conductivities is finally proposed and validated in the paradigmatic cases of elemental and molecular fluids (liquid Ar and H2O) and of crystalline and glassy solids (MgO and a-SiO2).
 L. Ercole, A. Marcolongo, and S. Baroni, Heat transport coefficients from optimally short molecular dynamics simulations, submitted, arXiv:1706.01381 [cond-mat.stat-mech].