• statistichal mechanichs
• money
• exchange
• econophysics
• ABM
• wealth
• Yakovenko

This thesis aims at bringing together the complexity of ABMs with the simple mathematical description of econophysics in order to address the issue of economic inequality and wealth distribution in the long run, in a similar fashion to what the economist Thomas Piketty did in his book “Capital in the 21st century”.
This is achieved in two ways:
- Developing new mathematical tools and frameworks to apply the econophysics model of Dragulescu & Yakovenko (DY model) to real world phenomena like the study of social mobility and the development of optimal fiscal and monetary policy.
- Creating a new model of capital exchange based on the DY model in which the contribution of financial investments, consume, income and taxes are implemented.

The final objective of this thesis will be of practical nature: to address fiscal and monetary policies. But in doing so, a wide range of physical ideas will come to life: trade will be explained with thermodynamics, social mobility will be studied with Brownian motion and path integrals, fiscal policy will be discussed with the Euler-Lagrange equations, and monetary policy will reveal a phenomenology
for the DY model quite similar to bands in crystals.