Equilibrium in the economic potential picture

It might have been a bit confusing to see $N$ on both sides of the second equation in this post. That's because I used an equilibrium relationship to solve for the $T S$ term. If you use an equilibrium relationship for all three terms you actually come out with all the terms being proportional to $N$. Let's see how that works ...

We start with

$$
N \approx c N/\kappa + \kappa P M + \alpha p X
$$

For the second term, we have

$$
\kappa P M = \kappa \frac{P_{0}}{\kappa} \left( \frac{M}{M_{0}} \right)^{1/\kappa - 1} M
$$
$$
 = \kappa \frac{P_{0}}{\kappa} \left( \frac{M}{M_{0}} \right)^{1/\kappa - 1} M_{0} \frac{M}{M_{0}}
$$
$$
= P_{0} M_{0} \left( \frac{M}{M_{0}} \right)^{1/\kappa}
$$
$$
= P_{0} M_{0}  \frac{N}{N_{0}} \equiv \eta N
$$

And for the third term, assuming the market $p : N \rightarrow X$ with information transfer index $k$, we have

$$
\alpha p X = (\alpha/k) N \equiv \gamma N
$$

Putting this all together, we have:

$$N \approx c N/\kappa + \eta N + \gamma N$$

$$ = ( c/\kappa + \eta + \gamma ) N $$

or

$$c/\kappa + \eta + \gamma \approx 1$$

with each constant term representing the fractional contribution of each piece of the economy; in this case: entropy (i.e. macro gains from having a large diverse economy), money and goods.