The traditional Green-Kubo (GK) expression based on the fluctuation dissipation theorem relates the thermal conductivity to the time integral of the heat auto correlation function. While popularly adopted in molecular dynamics (MD) simulations, modal and statistical analyses are not easily performed using the conventional GK algorithm. In this work, we recast the GK formalism based on the covariance of the heat current to extract the different eigenmodes from a principal component analysis (PCA). We first show that the evolution of the heat current can be represented as a linear superposition of only a few dominant modes using MD simulations; diamond and graphite serve as test materials. As the thermal conductivity is proportional to the ratio of the variance to the square of the temperature, the observed linear relationship of standard deviation with temperature indicates that the variation of conductivity with temperature can only arise from a change in the correlation decay time and not the initial correlation. We further discuss some of the advantages of the covariance form for performing error and sensitivity analyses.

Thermal conductivity and reduced-order approximation based on covariance of heat current

253rd National Meeting (2017)

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