Conductivity Equations Based on Rate Process Theory and Free Volume Concept for Addressing Low Temperature Conductive Behaviors like Superconductivity

New conduction equations are derived on the basis of Eyring’s rate process theory and free volume concept. The basic assumptions are that electrons traveling from one equilibrium position to the other may obey Eyring’s rate process theory; the traveling distance is governed by the free volume available to each electron by assuming that electrons may have a spherical physical shape with an imaginative effective radius. The obtained equations predict that the superconductivity happens only when electrons form certain structures of a relative small coordinate number like Cooper pair at low temperatures; If each electron has a large coordinate number such as 8 when electrons form the body-centered-cubic (bcc) lattice structure like Wigner crystal, the predicted conductivity decreases instead increases when temperatures approach to zero. The electron condensation structures have a big impact on the conductivity. A sharp conductivity decrease at low temperatures, probably due to an Anderson transition, is predicted even when the Cooper pair is formed and the electrons can only travel short distances; While the Mott transition appears when crystalline structures like Wigner crystal form. On the other hand, the electron pairing or called the strong spin-spin coupling is predicted to induce Kondo effect when electrons are assumed to travel a very short distance. The Anderson localization seems to have a lot of similarities as Kondo effect such as electron pairing and low traveling distances of electrons at low temperatures. The Cooper pair that is the essence of BCS theory for superconductivity and the spin-spin coupling that is the cause for Kondo effect seem to contradict each other, but are seamlessly united in our current conductivity equations. The topological insulators become the natural occurrences of our equations, as both Kondo insulator and superconductivity share a same physical origin–the electron pairs, but the electrons just travel different distances at these two cases. A material containing an element of a high electro-negativity (or high ionization energy) and an element of a low electro-negativity(or low ionization energy) may form a good topological insulator and superconductor. Any magnetic element, like Iron, Nickel, and Cobalt, that has unpaired electrons and can induce Kondo effect as a dopant, could be a very good superconductor candidate once it is synthesized together with other proper elements of low electronegativity (for example forming pnictide superconductors). The numbers of both conduction and valence electrons and the volume of a material under investigation have positive impacts on the conductivity. Any method that may increase the numbers of both conduction and valence electrons may move the superconductivity transition temperatures to higher regions. Any method that may reduce the volume of the material like external pressure seems to lower transition temperatures,