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Thermal conductivities are routinely calculated in molecular dynamicssimulations by keeping the boundaries at different temperatures and measuringthe slope of the temperature profile in the bulk of the material, explicitlyusing Fourier's law of heat conduction. Substantiated by the observation of adistinct linear profile at the center of the material, this approach has alsobeen frequently used in superdiffusive materials, such as nanotubes or polymerchains, which do not satisfy Fourier's law at the system sizes considered. Ithas been recently argued that this temperature gradient procedure yields worseresults when compared with a method based on the temperature difference at theboundaries -- thus taking into account the regions near the boundaries wherethe temperature profile is not linear. We study a realistic example,nanocomposites formed by adding boron nitride nanotubes to a polymer matrix ofamorphous polyethylene, to show that in superdiffusive materials, despite theappearance of a central region with a linear profile, the temperature gradientmethod is actually inconsistent with a conductivity that depends on the systemsize, and, thus, it should be only used in normal diffusive systems.

Temperature gradient and thermal conductivity in superdiffusive materials