We present a rigorous approach that leads, from a many-particle description, to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at nanoscale. By enforcing statistical consistency, in that the statistics of the local energy is consistent with that from an all-atom description, we identify the driving force as well as the model parameters in these generalized constitutive models.
Categories: cond-mat.stat-mech math.PR