Third order dielectric time dependent susceptibilities and the "box model"

We present here the calculation of the "time dependent" moduli of the third order, dielectric, susceptibilities measured at the frequency ω of the applied electric field and at the frequency 3ω. The calculation is performed within the frame work of the "box model," both in the ideal case of a pure third order polarization and in the practical case studied by Samanta and Richert [J. Chem. Phys. 140, 247101 (2014)] where a first order polarization contribution is also detected. We show that, in the two cases, those two modules have a largely different dynamics and that the results can be easily compared with experiments thanks to the data gathered by Samanta and Richert [J. Chem. Phys. 140, 247101 (2014)]. This should provide a new test on the validity of the "box model."