A Theory of money in a maximally efficient economy

 I think we just need to make q = -log(p), where 1/p means small prices happen more often.  When that condition is met then we are at minimum redundancy. That is the distribution network is a minimum spanning tree. Each of the set of -1/p*log(p) is equally variant. So this assumes package sizes are set such that the purchase price for one collection of things is as variable as the purchase price for any other set of things.  IE, the purchase of a carton of eggs for $4 should be as uncertain as the purchase of a used truck for $6000, for example. Uncertainty is tricky, it means that the next transaction counted over the aggregate, would be as unpredictable as any other. So, we expect more cartons of eggs purchased than used trucks. But if the price of eggs for some transaction was $6, we would be more surprised than if the truck was $6200.

Then M*Vt is the entropy of the system. See Shannon Entropy. I think I have that, but as usual double check me.

Entropy does not decrease, in a closed economy, they say. An open economy can decrease its entropy with redundant transactions. How do we manage to increase our transaction rate (Vt) over the time? More categories of goods make for more complex network. Where are transaction costs? They are a multiplier on P, and split between P and -log(P). If you have high transaction costs then you have to raise price and increase quantity. If you give all the transactions an efficiency shock then they will rearrange sizes and prices and that restructuring is a recession. Rearranging transaction sequences is OK as long as you mostly keep the inter arrival separation, don't make them bunch up. Keeping them mostly separated while rearranging is called adiabatic.

For some reason
We have this encourage  the central banker to suppress the pricing mechanism, on purpose. We call it the 'price puzzle', meaning that the federal banker acting constantly against its boundaries should not crowd out the flow of money. But it does. It forces a slant across the pricing, and the economy gets redundant. We do this mostly to suppress the equalization of energy prices, and other imports, across the economy. Its a form of price control, and we call it a 'price puzzle'. Then when the Fed quits lending money and allows equalization we get a sudden inflation and price equalization. Its no puzzle.

The process is sort of logical.

I mean, energy prices are too high, so why not lower all prices by suppressing the price of short term money and extracting money from the economy.  Its as logical as any other price control that government tries.  The real puzzle is why economists call it a price puzzle. Its an attempt by government to suppress prices, and government does it all the time. No reason to be puzzled.

If the Fed wants to raise prices.
It should borrow money, borrow short term, borrow a lot of it. The interest it pays will fill the economy with free cash, and the principle is returned back to the economy, a net flow from the printing press to the economy.