Statistical ensembles for money and debt

Abstract

We build a statistical ensemble representation of two economic models describing respectively, in simplified terms, a payment system and a credit market. To this purpose we adopt the Boltzmann-Gibbs distribution where the role of the Hamiltonian is taken by the total money supply (i.e. including money created from debt) of a set of * Corresponding author 1 interacting economic agents. As a result, we can read the main thermodynamic quantities in terms of monetary ones. In particular, we define for the credit market model a work term which is related to the impact of monetary policy on credit creation. Furthermore, with our formalism we recover and extend some results concerning the temperature of an economic system, previously presented in the literature by considering only the monetary base as conserved quantity. Finally, we study the statistical ensemble for the Pareto distribution.

A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory

“…The corresponding multiplier is β. By imposing the further constraints on the strength sequences w out , w in with Lagrange multipliers {λ i }, {θ i }, we obtain that ǫ ij = λ i + θ j in (16). This is the Park & Newman model (PNM).…”

“…A recent stream of literature employs the techniques of statistical mechanics under the hypothesis that in a limited period of time an economic system may behave as though in a quasi-equilibrium state [3,4,5,6,7,8,9,10,11,12,13,14,15,16]. In these models we have homogeneous agents randomly exchanging money with a constraint on the total amount of money M in the system.…”

“…(16), instead, energy exchange can be obtained by a change in the number of links L. A variation of L, which represents a net inflow or outflow of commodities, has a clear interpretation in terms of open economic systems. Then we are naturally brought to wonder which are the economic implications of reversible transformations, i.e.…”

Effect of Savings on a Gas-Like Model Economy with Credit and Debt

“…Credit and debt are introduced through a new variable different from the money coming from income, in such a way that it could take negative values to a minimum, indicating the acquired debt. The economic model, including credit and debt, was first studied by Viaggiu et al using the tools of the statistical ensembles [7]. There they adopt the Boltzmann-Gibbs distribution where energy is replaced by total money, including income, credit, and debt.…”

Limit order book and its modeling in terms of Gibbs Grand-Canonical Ensemble

“…with economical concepts. Of particular interest here is the possibility of applying the Gibbs theory of Canonical Ensembles, which are at the core of the statistical treatment of thermodynamics, to the behavior of financial markets ( [3], [4]). As quoted in [4], "certainly the economy is a big statistical system with millions of participating agents and so presents itself as a possible and promising target for the application of statistical mechanics.…”