  Memristors are expected to form a major cornerstone in the upcoming
renaissance of analog computing, owing to their very small spatial footprint
and low power consumption. Due to the nature of their structure and operation,
the response of a memristor is intrinsically tied to local variabilities in the
device. This characteristic is amplified by currently employed semiconductor
fabrication processes, which introduce spatial inhomogeneities into the
structural fabric that makes up the layers of memristors. In this work, we
propose a novel q-deformed current-voltage model for memristors based on the
superstatistics framework, which allows the description of system-level
responses while taking local variabilities into account. Applied on a Ag-Cu
based synaptic memory cell, we demonstrate that our model has a 4-14% lower
error than currently used models. Additionally, we show how the resulting
q-parameter can be used to make statements about the internal makeup of the
memristor, giving insights to spatial inhomogeneities and quality control.
