Military fiat is a process whereby a decision is made and enforced by military means without the participation of other political elements. The Latin term fiat, translated as "let it be," suggests the autocratic attitude ascribed to such a process. For example, many coups involve the imposition of a new government by military fiat.
Origin of government
Historically, military fiat had no relation to particular theories of economics or how to use the power of the state ("political science"). It was simply seized by the powerful with some support from empowered citizens - typically resulting in a monarchy where power was passed on to heirs with no public consultation. Over time, this evolved into consultative systems, e.g. of other nobles holding fiefdoms, e.g. of public in parliaments.
In democracies, however, the political parties who run for office to represent the public will, must agree to certain guarantees to use power for public good - the relation between military and police powers is clearer but not obvious. In all countries, some fundamental decisions are made by the administration "without the participation of other political elements", and in general the administration of money has been one of those functions. Public recourse is limited if the state relies on any other nation for major military support, e.g. then-communist Poland's and East Germany's reliance on the Soviet Union. So "a decision is made and enforced by military means" could be anything done by the administration or bureaucracy as a normal part of its foreign policy.
Definition of participation
Theories vary on how to measure "participation of other political elements."
In economics, fiat is one of three ways to guarantee the value of money, credit money and commodity money being alternatives - but both relying to some degree on the fiat. True fiat money has no trust or product value of its own, but is backed only by trust in the issuing government and its ability to collect taxes or require conversion of some other resource into currency.
This view is questioned by some theories of political economy that argue that there is always some intrinsic reliance on trust, or expectation of the delivery of the commodity itself. Critics of these views argue that withholding taxes in domestic trade or defying powerful nations regarding trade in narcotics or arms will very rapidly prove dangerous or fatal to some of the participants - and, furthermore, that at least some of these decisions are unpopular and are not reflective of the public will. This is a common accusation made by the anti-globalization movement which argues that governments have been elected on a mandate to oppose global free trade and instead pursued it.
Military vs. monetary
The use of the military fiat to back economic transactions is what a given theory of political economy actually justifies, e.g. in the political economy of capitalism, military force is justified by the protection of property rights (which are presumed to optimize economic outcomes). Adam Smith defined "defense, infrastructure, justice, education and a stable currency" as the role of government. All defined, in his time, 1776, strictly by a military fiat in most countries, although Britain had a nascent democracy. When the United States broke with the British Empire and its military hegemony in that same year, it was to establish a fiat of its own.
Smith wrote specifically against monetarism, where fiat would be exploited to protect favored industries, monopolize precious metals, and other goals that were not generally shared between the state and the more general public.