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 economist's 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.