Statistical ensembles for money and debt

TL;DR

This paper develops a statistical ensemble framework for economic models of payment systems and credit markets, linking thermodynamic concepts to monetary quantities and analyzing the effects of monetary policy.

Contribution

It introduces a novel ensemble approach using the Boltzmann-Gibbs distribution to connect thermodynamics with monetary economics, extending previous models.

Findings

Thermodynamic quantities are expressed in terms of monetary variables.

The impact of monetary policy on credit creation is quantified as a work term.

The formalism extends to the Pareto distribution, broadening its applicability.

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 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.