I think you are correct in that you don’t actually have to have 1 electron per electron-radius (~nm) of wire—you could have a segment that is longer, but I think if you work that out it requires larger voltages to actually function correctly in terms of reliable transmission. This is all assuming we are using electron waves to transmit information, rather than ballistic electrons (but the Landauer limit will still bound the latter, just in a different way).
If you look at the spherical cow (concentric cylinder wire model), for smallish wires it reduces effectively to a constant that relates distance to capacitance, with units farads/meter.
The Landauer/Tile model predicts in advance a natural value of this parameter will be 1 electron charge per 1 volt per 1 electron radius, ie 1.602 e-19 F / 1.23 nm, or 1.3026 e-10 F/m.
So, capacitance of wires! Capacitor energy is QV/2, or CV^2/2. Let’s make a spherical cow assumption that all wires in a chip are half as capacitive as ideal coax cables, and the dielectric is the same thickness as the wires. Then the capacitance is about 1.3*10^-10 Farads/m (note: this drops as you make chips bigger, but only logarithmically).
The probability that the Landauer/Tile model predicts the same capacitance per unit distance while not also somehow representing the same fundamental truth of nature, is essentially epsilon. Somehow the spherical wire capacitance model and the spherical tile electron radius Landauer/Tile model are the same.
I think you are correct in that you don’t actually have to have 1 electron per electron-radius (~nm) of wire—you could have a segment that is longer, but I think if you work that out it requires larger voltages to actually function correctly in terms of reliable transmission. This is all assuming we are using electron waves to transmit information, rather than ballistic electrons (but the Landauer limit will still bound the latter, just in a different way).
If you look at the spherical cow (concentric cylinder wire model), for smallish wires it reduces effectively to a constant that relates distance to capacitance, with units farads/meter.
The Landauer/Tile model predicts in advance a natural value of this parameter will be 1 electron charge per 1 volt per 1 electron radius, ie 1.602 e-19 F / 1.23 nm, or 1.3026 e-10 F/m.
The probability that the Landauer/Tile model predicts the same capacitance per unit distance while not also somehow representing the same fundamental truth of nature, is essentially epsilon. Somehow the spherical wire capacitance model and the spherical tile electron radius Landauer/Tile model are the same.