Tracking the Taxonomy of QM

From the Hydraulic model to the Dual Norms model.

Infinite dimensional, reversible flow. This is the hydraulic model with no inventories, an infinite stages of production, smoothly changing. The result is all goods distributions have smooth Gaussian yield curves. No shock can harm the system because we can costlessly repossess and disassemble products and put their components into inventory. Everything is visible and firms minimize inventory variance. This is the minimum Variance Norm. If we add hidden information, nothing changes except decay processes are known ex post.

I suggest following the physics standard and put decay processes on the right side of any yield curve where they have negative sign.

The next addition is positive definite flow, little reversibility. This introduces inventories and the Zero Bound problem. But the Zero Bound problem still allows smooth changes as long as firms in the stages of production can costlessly merge and divide so as to avoid the bound.

Then I introduce the Constant Uncertainty, inventories at all levels of production will have the same variance. This introduces the market, for the first time, in my opinion. Markets exist so the stages of production can negotiate the size and frequency of goods shipments to meet constant uncertainty. This introduces the Shannon coding problem of the market and introduces the Entropy Norm.

Up through hydraulic macro, the simple mechanics of minimizing inventory variances was the main concern. Inventories were allowed to grow in reasonable size, even the Zero Bound was handled. In these conditions, the economy simply act like a hydraulic flow with local adjustments promising to lead to global adjustments. Hence, no real need for markets, whether truck and barter or monetary.

References:

Here I perform a selective web search of Entropy based economic studies. I limit references to studies the utilize entropy coding in markets, excluding the theories based on general thermodynamic entropy. The two themes should be resolved, but not by me right now.

Mistrulli:

"Interbank markets allow banks to cope with specific liquidity shocks. At the same time, they may be a channel allowing a bank default to spread to other banks. This paper analyzes how contagion propagates within the Italian interbank market using a unique data set including actual bilateral exposures. Since information on bilateral exposures was not available in most previous studies, they assumed that banks spread their lending as evenly as possible among all the other banks by maximizing the entropy of interbank linkages. Based on the data available on actual bilateral exposures for all Italian banks, the results obtained by assuming the maximum entropy are compared with those reflecting the observed structure of interbank claims. The comparison indicates that, in line with the thesis prevailing in the literature, the maximum entropy method tends to underestimate the extent of contagion. However, this does not hold in general. Under certain circumstances, depending on the structure of the interbank linkages, the recovery rates of interbank exposures and banks’ capitalization, the maximum entropy approach overestimates the scope for contagion."

Daroonerh:

Actually develops the entropy model for insurance networks, still reading this one.

Totonto prediction Blog:
Measuring Entropy in prediction markets.

Phillippatos and Wilson:
State Weighted Entropy as a Measurement of portfolio risk.

Reesor and McLeish:
Uncertainty in financial markets: Can entropy be a solution?

And we should read the work of Kelly, Entropy and Gambling discussed in this Wiki.