On the futility of the Fuoss-Kirkwood relation

The Fuoss-Kirkwood (FK) relation is used to derive analytical expressions for the distribution of uncorrelated relaxation times (DRT), particularly of probed biochemical and electrochemical systems, often without scrutiny. Its futility is proven simply by using the parity of impedance with complex frequencies. However, given the futile nature of the FK relation, these expressions are not suitable for validation of computed DRT spectra. Despite this, the need for such expressions persists. Addressing this need and the oversight of the dependency of the DRT value on the underlying data, the DRT is extended into the complex plane using the Hilbert transform (HT). It makes the DRT universal for any complex-valued quantity to not only quantify the extent of relaxations but also to assess their nature. keyword: distribution; integral transforms; relaxation time; superposition.