Transfer Potentials shape and equilibrate Monetary Systems

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economists quantity theory (MV=PQ). To match the resulting quantity of money with the model assumption of a constant price, we have to impose boundary conditions. They either restrict specific transfers globally or impose transfers locally. Both connect through a general framework of transfer potentials. We show that either restricted or imposed transfers can shape gaussian, tent-shape exponential, boltzmann-exponential, pareto or periodic equilibrium distributions. We derive the master equation and find its general time dependent approximate solution. An equivalent of quantity theory for random money transfer under the boundary conditions of transfer potentials is given.