Anomalous heat diffusion

Abstract

Consider anomalous energy spread in solid phases, i.e., Δx2(t)≡∫(x-x)2ρE(x,t)dx tβ, as induced by a small initial excess energy perturbation distribution ρE(x,t=0) away from equilibrium. The second derivative of this variance of the nonequilibrium excess energy distribution is shown to rigorously obey the intriguing relation d2Δx2(t)/dt2=2CJJ(t)/(kBT2c), where CJJ(t) equals the thermal equilibrium total heat flux autocorrelation function and c is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-like relation. Given that the averaged nonequilibrium heat flux is governed by an anomalous heat conductivity, the energy diffusion scaling determines a corresponding anomalous thermal conductivity scaling behavior. © 2014 American Physical Society.