# 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:

such that

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.