Description

This PhD proposal falls within the field of econophysics, which applies statistical physics tools to the study of economic systems. Since the foundational work of the Santa Fe Institute in the 1980s, it has been established that simple interactions between agents can generate robust statistical patterns, such as power-law wealth distributions. However, these models have largely overlooked the physical constraints underlying economic activity—energy and matter flows, as well as dissipation processes—which ultimately limit real-world production. This project aims to ground the dynamics of economic exchanges in an explicit physical framework, building on recent work by Herbert et al. (2023), which describes macroeconomic metabolism as a flow circulating between resource reservoirs and waste sinks, governed by thermodynamic laws.
The main objective is to investigate how microscopic exchange rules produce, at the collective level, characteristic wealth distributions while integrating the constraints imposed by energy and matter reservoirs. The thesis will explore the robustness of stationary distributions when exchange rules deviate from the ideal case, such as when agents retain a fraction of their wealth or when exchanges are proportional to the wealth held. It will also analyze non-conservative dynamics, where wealth can be injected into or withdrawn from the system, along with the resulting transient regimes and bifurcations. A model combining additive and multiplicative exchange mechanisms will be developed to reproduce empirically observed dual-regime distributions. Finally, the coupling between exchange dynamics and the state of physical reservoirs will link resource depletion to the evolution of economic inequalities, as measured by indicators like the Gini coefficient.
The methodology will rely on a multidisciplinary approach, combining mathematical modeling (kinetic equations, Markov chains), numerical simulations (agent-based models), and empirical data analysis. Collaborations with experts in macroeconomics and financial market analysis, such as Gaël Giraud and Jean-Philippe Bruneton, will enrich this work. This thesis stands out for its ambition to quantitatively link economic inequalities to energy and matter flows, paving the way for a more integrated understanding of economic systems where biophysical constraints play a central role.

Skills required

A degree in mathematics, mathematical physics, or energy engineering. Strong proficiency in mathematical modeling tools and dynamical systems, with training in probability theory, Markov chains, thermodynamics, transport phenomena, and multiphysics modeling. A keen interest in mathematics, non-equilibrium complex systems, and modeling is essential. No prior background in economics is required.

Bibliography

Adrian Drăgulescu and Victor M. Yakovenko. Statistical mechanics of money. The European PhysicalJournal B, 17 :723–729, 2000. doi : 10.1007/s100510070114.
[2]Victor M. Yakovenko and J. Barkley Rosser. Colloquium : Statistical mechanics of money, wealth,and income. Reviews of Modern Physics, 81 :1703–1725, 2009. doi : 10.1103/RevModPhys.81.1703.
[3]Éric Herbert, Gaël Giraud, Aurélie Louis-Napoléon, and Christophe Goupil. Macroeconomic dynamicsin a finite world based on thermodynamic potential. Scientific Reports, 13 :18020, 2023. doi :10.1038/s41598-023-44699-y
[4]Anirban Chakraborti and Bikas K. Chakrabarti. Statistical mechanics of money : how savingpropensity affects its distribution. The European Physical Journal B, 17 :167–170, 2000. doi :10.1007/s100510070173.
[5]Hugo Touchette. The large deviation approach to statistical mechanics. Physics Reports, 478 :1–69,2009. doi : 10.1016/j.physrep.2009.05.002.
[6]Thomas Piketty and Emmanuel Saez. Income inequality in the United States, 1913–1998. TheQuarterly Journal of Economics, 118 :1–39, 2003. doi : 10.1162/00335530360535135.
[7]Robert U. Ayres and Benjamin Warr. The Economic Growth Engine : How Energy and Work DriveMaterial Prosperity. Edward Elgar Publishing, Cheltenham, 2010.
[8]Emmanuel Bovari, Gaël Giraud, and Florent McIsaac. Coping with collapse : a stock-flow consistentmonetary macrodynamics of global warming. Ecological Economics, 147 :383–398, 2018. doi :10.1016/j.ecolecon.2018.01.034

Keywords

Non-equilibrium thermodynamics, Dissipative structures