Abstract We propose a method for deducing the parameters of the non-linear relaxation distribution model from isothermal measurements. Following this thermodynamic theory, isothermal relaxations can be described as isokinetic processes over a reduced time scale, taking into account non-linear effects, i.e. integrating the sample history. The proposed method leads to the definition of three characteristic parameters of this new time scale. In addition, the model predicts a universal shape of relaxation spectrum for frozen-in fluctuations. Applying this method to magnetostriction changes in Vitrovac® 6025 (Co 67Fe 4Mo 1.5Si 16.5B 11), we are able to simulate various thermal histories starting from high temperature equilibrium in the liquid state. We found good agreement with experiments. Free-energy spectra are determined.