The memristor (a portmanteas of "memory resistor") was originally envisioned in 1971 by circuit theorist Leon Chua as a missing non-linear passive two-terminal electrical component relating electric charge and magnetic flux linkage. According to the governing mathematical relations, the memristor's electrical resistance is not constant but depends on the history of current that had previously flowed through the device, i.e., its current resistance depends on how much electric charge has flowed in what direction through it in the past. The device remembers its history, that is, when the electric power supply is turned off, the memristor remembers its most recent resistance until it is turned on again.

Thermodynamic considerations, however, show that such a memristor component cannot exist as a solid state device in physical reality because its behavior would be inconsistent with fundamental laws of non-equilibrium thermodynamics.

Leon Chua has more recently argued that the definition could be generalized to cover all forms of 2-terminal non-volatile memory devices based on resistance switching effects although some experimental evidence contradicts this claim, since a non-passive nano-battery effect is observable in resistance switching memory. Chua also argued that the memristor is the oldest known circuit element with its effects predating the resistor, capacitor and inductor. SK Hynix and HRL Laboratories.

In 2008, a team at HP Labs claimed to have found Chua's missing memristor based on an analysis of a thin film of titanium dioxide. However, some skepticism has been expressed regarding this analysis. These devices are intended for applications in nano-electronic memories, computer logic and neuromorphic computer architectures. In October 2011, the team announced the commercial availability of memristor technology within 18 months, as a replacement for Flash, SSD, DRAM and SRAM. Commercial availability was more recently estimated as 2018. In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip.

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