Theory and Numerical Simulation of Heat Transport in Multicomponent Systems

The thermal conductivity of classical multicomponent fluids is seemingly affected by the intrinsic arbitrariness in the definition of the atomic energies, and it is ill conditioned numerically, when evaluated from the Green-Kubo theory of linear response. To cope with these two problems, we introduce two new concepts: a convective invariance principle for transport coefficients, in the first case, and multivariate cepstral analysis, in the second. A combination of these two concepts allows one to substantially reduce the noise affecting the estimate of the thermal conductivity from equilibrium molecular dynamics, even for one-component systems.

Figure 1

Energy flux of a water-ethanol mixture. Gray: Energy-flux sample power spectrum from a 100 ps trajectory. Red and blue lines: Moving averages over a window of 0.2 THz of the energy-flux power sample spectrum and of the SCCB of the sample cross-spectrum, computed from a long (28 ns) trajectory. Inset: Low-frequency region of the spectrum.

Figure 2

Thermal conductivity of a water-ethanol solution [Eq. (4)] as a function of the upper limit of integration in Eq. (2). The shaded areas indicate the estimated statistical error. Green: Direct estimate from Eqs. (2) and (4). Orange: Estimate from the Einstein-Helfand relation; see the main text. Purple: Cepstral analysis estimate.

Figure 3

Multivariate analysis of ab initio water. The sample power spectrum of the DFT energy flux would be out of scale and numerically intractable. Blue: SCCB of a two-component analysis performed with the total momentum of the oxygen atoms as an inert flux. Orange: Three-component analysis, where the third flux is the electronic adiabatic current. Both are filtered with a moving average of width 1 THz. In the inset, the spectrum obtained from cepstral analysis is displayed in dashed lines.