Geometrothermodynamic approach in econophysics

Abstract

The formalism of geometrothermodynamics has been developed to describe the properties of thermodynamic systems in terms of concepts of differential geometry. On the other hand, in econophysics, it is argued that under certain conditions the behavior of economic systems can be described by using the laws of classical thermodynamics. These two results are used in this work to propose a geometric description of economic systems. We obtain as a result that most systems can be described by two different geometries corresponding to the Boltzmann–Gibbs and Pareto distributions, which represent two different population groups that are usually present in most economic systems. The geometrothermodynamic analysis shows that no phase transitions are present in the Boltzmann–Gibbs sector, whereas the Pareto sector is characterized by a strong thermodynamic interaction that leads to the appearance of a rich phase transition structure. We argue that those phase transitions could be interpreted as financial crises.