The Poisson higher moments

Stirling numbers of the second kind

These give you the finite log map when the input, output chyoices are greater than two, and they appear in the higher moments of the Poisson.

In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by or .^[1] Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the study of partitions.

In other words, Shannon says you have one or two items in the queue, that makes symmetric entropy. But that not need be true all the time.  In fact, there is a generalized sampling theorem out there somewhere, if I looked.
But these numbers appear in the higher moments of the Poisson:

Lamda is really the transaction rate for the aggregate in a maximum entropy structure. In economics we are interested in the second and third moment, symmetry and skew. It is perfectly reasonable for organizations to keep three elements in the queue, and allow a cubic entropy function.  Three elements in the queue means the queue gain goes as lambda to the cubed power, and the number of sets any node in the map has is the sum of the Stirling numbers up to three. The node in the flow has a three gate distribution output. The entropy in this case is a third order, likely all we need for economics. And it is easy for some genius, like Jerry Brown, to go and fit his moment in there, between New York and Texas; he'd be damn good at triangulation.