Electrical charge in nanoelectronic circuit elements – resistors, capacitors, and inductors - is explained by the quantum mechanics (QM) requirement that specific heat vanishes in nanostructures. In the memristor, Joule heating therefore cannot be conserved by an increase in temperature. Instead, conservation proceeds by the QED induced creation of photons within the TIR confinement frequency of the memristor. QED stands for quantum electrodynamics and TIR for total internal reflection. The TIR confinement of QED photons is enhanced by the fact the absorbed energy concentrates in the TIR mode by the high surface to volume ratio in nanostructures. The QED photons having Planck energy beyond the ultraviolet produce excitons, the electrons and holes of which reduce the initial resistance of the memristor, but the resistance is recovered later in the same cycle as the electrons and holes are attracted to and destroyed by the polarity of the voltage terminals.
Early simulations  of the Hewlett-Packard (HP) memristor used an approximate integration of the differential equation for the QED induced creation and trapping of holes during a cycle of sinusoidal voltage. See PR’s at http://www.prlog.org/
Update the hole response for the HP memristor with improved numerical solutions. Extend the QED induced radiation in nanoscale heat transfer for the HP memristor to other nanoelectronics elements including nanowire memristors, the Ovshinsky Effect, phase-change random access memory (PCRAM), and ballistic transport in nanocontacts. Nanocars are included to illustrate the generality of QED heat transfer at the nanoscale.
Updated Numerical Simulation
The updated HP memristor simulation  giving I-V curves illustrated in the thumbnail shows reasonable agreement with the HP data. See Paper at http://www.nanoqed.org at "Electrical Charge in Nanoelectronics,"
Summary and Conclusions
1. The original paper by Chua and others to date are classical approaches in explaining memristor behavior. But a QM approach is suggested at the nanoscale where memristive effects are observed.
2. QED radiation developed for heat transfer in nanostructures based on QM is directly applicable to memristors by precluding any temperature increases to conserve Joule heat. Conservation proceeds by the production of QED photons inside the memristor that create the space charge of electrons and positive charged holes that produce the memristive effect.
3. In the HP memristor, the simulations show Joule heat is mostly loss to the surroundings, and only a small fraction creates excitons. At 5 kHz and mobility 10^-6 and 10^-8 cm2/V-s, the fraction is about 10^-8. Since the photoelectric yield of TiO2 is of order 10^-2, the exciton yield from QED photons should be much higher. What this means is most QED photons are simply lost from the ultra-thin TiO2 film.
4. The mobility of 0.05 cm2/V-s for electrons and holes in TiO2 given in the literature appears at least 4 orders of magnitude higher than necessary to fit the HP data. More study is required.
5. Generally, explanations of memristive effects need not rely on oxygen vacancies, electromigration thinning, unexplained space charge, and the like. Reduced resistance in PCRAM films by high temperature melting from laser and current pulses may be negated by QM. Further study is required.
6. Ballistic heat transport across nanocontacts is negated by QED heat transfer as QM precludes temperature changes.
7. Memristors have nothing to do with the notion of the missing fourth element necessary to provide completeness for the symmetry of the resistor, capacitor, and inductor. Instead, memristor behavior is simply a QM size effect.
 Prevenslik, T., “Memristors by Quantum Mechanics,” International Conference on Intelligent Computing, ICIC 2011, Zhengzhou, 11-14 August, 2011.
 Prevenslik, T., “Quantum Mechanics and Nanoelectronics,”
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About QED Induced EM Radiation: Classically, absorbed EM energy is conserved by an increase in temperature. But at the nanoscale, temperature increases are forbidden by quantum mechanics. QED radiation explains how absorbed EM energy is conserved at the nanoscale by the emission of nonthermal EM radiation.