Stochastic memory: memory enhancement due to noise

There are certain classes of resistors, capacitors and inductors that, when subject to a periodic input of appropriate frequency, develop hysteresis loops in their characteristic response. Here, we show that the hysteresis of such memory elements can also be induced by white noise of appropriate intensity even at very low frequencies of the external driving field. We illustrate this phenomenon using a physical model of memory resistor realized by $\mathrm{TiO_2}$ thin films sandwiched between metallic electrodes, and discuss under which conditions this effect can be observed experimentally. We also discuss its implications on existing memory systems described in the literature and the role of colored noise.