Rent's Rule and Information Equilibrium
Another application of information equilibrium
Rent’s rule is a heuristic relationship between the number of “pins” (“terminals” below) and the number of “gates” in logic blocks in a computing architecture — one that is surprisingly robust. There is even a theoretical basis that is surprisingly similar to the derivation of the information equilibrium condition:
The paper goes on to add a parameter p that is related to the topology of the circuit. Taking the information equilibrium approach we would posit that if T and G are in information equilibrium T ⇄ G — i.e. the information in the distribution of states of the gates “G” is equal to the information in the distribution of the states of the terminals “T” then:
where T₀ and G₀ are constants of integration. Alternatively:
The topology parameter p is the information transfer index.
What is also interesting is that in “Region II” for larger values of G (figure from here where B for blocks is used instead of G for gates, and P for pins is used instead of T for terminals) the value starts to fall below the heuristic estimate:
In the information transfer framework, this is indicative of non-ideal information transfer and we would derive (using Gronwall’s inequality):
This gives us another analogy to work with when understanding economic relationships (e.g. pins = demand, gates = supply). As a side note, I worked out some time ago that you can understand a transistor (including Early voltage and compression) using the information transfer framework as well.
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