Maximum entropy and the 'natural rate' of unemployment

I mentioned in this post that maximum entropy in the MINIMAC model gives us a pretty simple mechanism to generate a 'natural rate' of unemployment. Not a perfect model, but pretty good:

You'd imagine policy to kick in if the unemployment rate got to high (stimulus) or too low (tight money to reign in inflation), which would shape the distribution ... and there's the finite number of measurements ...
But it's a heck of simple model! Large number of consumption periods (D >> 1) + finite supply of labor (constraint L) = natural rate (L' < L). Just use this diagram (from here)