Last night dream:
Subnothing algebra: Consider a box filled with N billard balls like objects. Then the entropy of the N bilard balls (which are classical hence distinguishable) is given by $\textrm{ln}(N!)$.
These balls, however obey some kind of nonassociative interaction. Imagine grouping $k \leq N$ balls together, then these will nullify into nothing (represented by $0$ in the cutscene). The $0$ element, however is not an identity, since $0+0\neq 0$ but rather they act like a strange type of billard ball that will pile up in the box in an extensive manner.