When one wants to go beyond mere curve fitting and aims at a real physical modeling of non-volatile memory elements, e.g., resistive random-access memory devices, one has to keep an eye on the aforementioned physical correlations. To check the adequacy of the proposed model and its resulting state equations, the input signal u (t) can be superposed with a stochastic term ξ (t), which takes into account the existence of inevitable thermal fluctuations. The dynamic state equation in its general form then finally reads: