Thermodynamics of inequalities: From precariousness to economic stratification

• Economic stratification is measured by the entropy of the wealth distribution.
• The fluctuation theorem implies a “second-law inequality” for stratification.
• Precariousness is the thermodynamic force conjugate to upward economic mobility.
• Precariousness and upward economic mobility together drive stratification up.
• We estimate the relaxation time of the wealth distribution in a diffusion model.

Growing economic inequalities are observed in several countries throughout the world. Following Pareto, the power-law structure of these inequalities has been the subject of much theoretical and empirical work. But their nonequilibrium dynamics, e.g. after a policy change, remains incompletely understood. Here we introduce a thermodynamical theory of inequalities based on the analogy between economic stratification and statistical entropy. Within this framework we identify the combination of upward mobility with precariousness as a fundamental driver of inequality. We formalize this statement by a “second-law” inequality displaying upward mobility and precariousness as thermodynamic conjugate variables. We estimate the time scale for the “relaxation” of the wealth distribution after a sudden change of the after-tax return on capital. Our method can be generalized to gain insight into the dynamics of inequalities in any Markovian model of socioeconomic interactions.