Yeah, I agree that once you take into account resistance, you also get a length scale. But that characteristic length is going to be dependent on the exact geometry and resistance of your transmission line. I don’t think it’s really possible to say that there’s a fundamental constant of ~1nm that’s universally implied by thermodynamics, even if we confine ourselves to talking about signal transmission by moving electrons in a conductive material.
There’s a wide spread of possible levels of attenuation for different cable types. Note the log scale.
A typical level of attenuation is 10dB over 100 ft. If the old power requirement per bit was about kT, this new power requirement is about 10kT. Then presumably to send the signal another 100ft, we’d have to pay another 10kT. Call it 100kT to account for inefficiencies in the signal repeater. So this gives us a cost of 1kT per foot rather than 1kT per nanometer!
That linked article and graph seems to be talking about optical communication (waveguides), not electrical.
There’s nothing fundamental about ~1nm, it’s just a reasonable rough guess of max tile density. For thicker interconnect it seems obviously suboptimal to communicate bits through maximally dense single electron tiles.
But you could imagine single electron tile devices with anisotropic interconnect tiles where a single electron moves between two precise slots separated by some greater distance and then ask what is the practical limit on that separation distance and it ends up being mean free path
So anisotropic tiles with length scale around mean free path is about the best one could expect from irreversible communication over electronic wires, and actual electronic wire signaling in resistive wires comes close to that bound such that it is an excellent fit for actual wire energies. This makes sense as we shouldn’t expect random electron motion in wires to beat single electron cellular automata that use precise electron placement.
The equations you are using here seem to be a better fit for communication in superconducting wires where reversible communication is possible.
That linked article and graph seems to be talking about optical communication (waveguides), not electrical.
Terminology: A waveguide has a single conductor, example: a box waveguide. A transmission line has two conductors, example: a coaxial cable.
Yes most of that page is discussing waveguides, but that chart (“Figure 5. Attenuation vs Frequency for a Variety of Coaxial Cables”) is talking about transmission lines, specifically coaxial cables. In some sense even sending a signal through a transmission line is unavoidably optical, since it involves the creation and propagation of electromagnetic fields. But that’s also kind of true of all electrical circuits.
Anyways, given that this attenuation chart should account for all the real-world resistance effects and it says that I only need to pay an extra factor of 10 in energy to send a 1GHz signal 100ft, what’s the additional physical effect that needs to be added to the model in order to get a nanometer length scale rather than a centimeter length scale?
Using steady state continuous power attenuation is incorrect for EM waves in a coax transmission line. It’s the difference between the small power required to maintain drift velocity against frictive resistance vs the larger energy required to accelerate electrons up to the drift velocity from zero for each bit sent.
In some sense none of this matters because if you want to send a bit through a wire using minimal energy, and you aren’t constrained much by wire thickness or the requirement of a somewhat large encoder/decoder devices, you can just skip the electron middleman and use EM waves directly—ie optical.
I don’t have any strong fundemental reason why you couldn’t use reversible signaling through a wave propagating down a wire—it is just another form of wave as you point out.
The landauer bound till applies of course, it just determines the energy involved rather than dissipated. If the signaling mechanism is irreversible, then the best that can be achieved is on order ~1e-21 J/bit/nm. (10x landauer bound for minimal reliability over a long wire, but distance scale of about 10 nm from the mean free path of metals). Actual coax cable wire energy is right around that level, which suggests to me that it is irreversible for whatever reason.
Yeah, I agree that once you take into account resistance, you also get a length scale. But that characteristic length is going to be dependent on the exact geometry and resistance of your transmission line. I don’t think it’s really possible to say that there’s a fundamental constant of ~1nm that’s universally implied by thermodynamics, even if we confine ourselves to talking about signal transmission by moving electrons in a conductive material.
For example, take a look at this chart:
(source) At 1GHz, we can see that:
There’s a wide spread of possible levels of attenuation for different cable types. Note the log scale.
A typical level of attenuation is 10dB over 100 ft. If the old power requirement per bit was about kT, this new power requirement is about 10kT. Then presumably to send the signal another 100ft, we’d have to pay another 10kT. Call it 100kT to account for inefficiencies in the signal repeater. So this gives us a cost of 1kT per foot rather than 1kT per nanometer!
That linked article and graph seems to be talking about optical communication (waveguides), not electrical.
There’s nothing fundamental about ~1nm, it’s just a reasonable rough guess of max tile density. For thicker interconnect it seems obviously suboptimal to communicate bits through maximally dense single electron tiles.
But you could imagine single electron tile devices with anisotropic interconnect tiles where a single electron moves between two precise slots separated by some greater distance and then ask what is the practical limit on that separation distance and it ends up being mean free path
MFP also naturally determines material resistivity/conductivity.
So anisotropic tiles with length scale around mean free path is about the best one could expect from irreversible communication over electronic wires, and actual electronic wire signaling in resistive wires comes close to that bound such that it is an excellent fit for actual wire energies. This makes sense as we shouldn’t expect random electron motion in wires to beat single electron cellular automata that use precise electron placement.
The equations you are using here seem to be a better fit for communication in superconducting wires where reversible communication is possible.
Terminology: A waveguide has a single conductor, example: a box waveguide. A transmission line has two conductors, example: a coaxial cable.
Yes most of that page is discussing waveguides, but that chart (“Figure 5. Attenuation vs Frequency for a Variety of Coaxial Cables”) is talking about transmission lines, specifically coaxial cables. In some sense even sending a signal through a transmission line is unavoidably optical, since it involves the creation and propagation of electromagnetic fields. But that’s also kind of true of all electrical circuits.
Anyways, given that this attenuation chart should account for all the real-world resistance effects and it says that I only need to pay an extra factor of 10 in energy to send a 1GHz signal 100ft, what’s the additional physical effect that needs to be added to the model in order to get a nanometer length scale rather than a centimeter length scale?
See my reply here.
Using steady state continuous power attenuation is incorrect for EM waves in a coax transmission line. It’s the difference between the small power required to maintain drift velocity against frictive resistance vs the larger energy required to accelerate electrons up to the drift velocity from zero for each bit sent.
In some sense none of this matters because if you want to send a bit through a wire using minimal energy, and you aren’t constrained much by wire thickness or the requirement of a somewhat large encoder/decoder devices, you can just skip the electron middleman and use EM waves directly—ie optical.
I don’t have any strong fundemental reason why you couldn’t use reversible signaling through a wave propagating down a wire—it is just another form of wave as you point out.
The landauer bound till applies of course, it just determines the energy involved rather than dissipated. If the signaling mechanism is irreversible, then the best that can be achieved is on order ~1e-21 J/bit/nm. (10x landauer bound for minimal reliability over a long wire, but distance scale of about 10 nm from the mean free path of metals). Actual coax cable wire energy is right around that level, which suggests to me that it is irreversible for whatever reason.