Multiscale Model for the Dielectric Permittivity

We present a generalisation of the Debye relaxation model for the dielectric permittivity in the case in which the global relaxation process is the result of many elementary excitations. The relaxation dynamics is in this case non-Markovian. In the case of many events, for which the central limit theorem holds and Gaussianity as well as the assumption of independency are both plausible, the global relaxation time is given by a log-normal function. The hierarchy of relaxation times leads to a generalised expression of the dielectric permittivity.