Think of money as some kind of material object used as a symbol to transfer value from someone else to the owner of the money.
The objects may be computer bits, paper documents, or whatever.
There are, of course, many ways of classifying money, but here I want to divide the money universe into coercive and non-coercive segments.
I would think non-coercive money would be what most people think of as ordinary money. It is a promise to deliver something of equivalent value. It is basically a promise to do good. It is a mechanism that strives to achieve balance and fairness.
Coercive money would be a promise to do bad such as a promise of some kind of attack. A letter from a lawyer is probably the most common form of such a document. But, just as the Eskimo has 11 words for snow, we have a lot of words for coercive money. There is the jury summons, the criminal indictment, tax bills, etc.
The amount of non-coercive money in circulation is determined by the available means of production of goods and services that people will pay to enjoy.
The amount of coercive money is determined by the destructive capabilities of the various armed and aggressive agents in a society. These would include armies, police agencies, and armed organizations of civilians, families, and individual civilians. Coercive money requires that some assaults be made continuously. The police force would soon loose all its income from fines if they never arrested anyone who didn't pay. The very great coercive value of the atomic bomb had to be demonstrated before a value could be assigned.
Similarly an organization that carries out every threat it issues would be at a competitive disadvantage. The government never arrests everyone who disobeys one of its laws. With the congress writing tens of thousands of pages of laws a year, the processing costs of such a policy would be prohibitive. Most citizens have never read any of these laws. They know that the only real crime is attracting the negative attention of an agent of the government, and obeying laws has a minimal amount to do with staying out of jail.
Many people take pride in the rule of law. They believe in the efficacy of threats, and the fiction that there is some rational computational process that can assure that the law can be fairly applied to all citizens. And many of them even believe that this process is being currently applied. I expect this is a logical fallacy that will eventually disappear, or maybe not so eventually.
Economists can measure the amount of non-coercive money with relative ease. They call it the Gross National Product.
Measuring the Gross National Threat would be a lot more difficult, but most would agree that the USA has a higher GNT than any other country on planet earth.
Some statistics that might correlate with the GNT would be imprisonment rate, number of arrests, tax rates, number of written laws, and, of course the size and capabilities of state recognized armed groups. Since a state derives its income from its coercive capabilities, it constantly tries to increase them. It wants to exchange coercive money for non-coercive money.
An organization that creates coercive money has more information processing challenges than an organization devoted to creating non coercive money. It needs to convince enemies that it has more destructive power than it really has. It also needs to surprise when carrying out raids, wars, or whatever the current euphemism is for armed assault. The culture of the coercive organization is one of deceit and secrecy. Deceit requires a lot more information processing capability than simply telling the truth.
Almost everyone and every organization must deal with both coercive and non-coercive transactions. Governments and violent criminal gangs are the most coercive organizations. Churches and clubs are the most non-coercive. We could view the system as an ecology with governments and criminal gangs as predators and the rest of us as prey. Just as the lion of Africa has a shorter lifespan than the elephant, Governments have a shorter life span than churches.