Differences in relaxation kinetics of ensembles having the same Preisach representations of response operators

Results of the numerical experiment for relaxation of ensembles of systems in a random potential are reported. The operator of rate-independent response of systems in the considered potentials has non-local memory and is exactly representable by its Preisach decomposition. It is shown that there may exist potentials having exactly the same response operators (and thus their Preisach spectra) but whose thermal relaxation kinetics is dramatically different. Bounds of possible differences for a particular choice of the random potential are given.