Measures of physical mixing evaluate the economic mobility of the typical individual

Measures of economic mobility represent aggregated values for how wealth ranks of individuals change over time. Therefore, in certain circumstances mobility measures may not describe the feasibility of the typical individual to change their wealth ranking. To address this issue, we introduce mixing, a concept from statistical physics, as a relevant phenomenon for quantifying the ability of individuals to move across the whole wealth distribution. We display the relationship between mixing and mobility by studying the relaxation time, a statistical measure for the degree of mixing, in reallocating geometric Brownian motion (RGBM). RGBM is an established model of wealth in a growing and reallocating economy that distinguishes between a mixing and a non-mixing wealth dynamics regime. We show that measures of mixing are inherently connected to the concept of economic mobility: while certain individuals can move across the distribution when wealth is a non-mixing observable, only in the mixing case every individual is able to move across the whole wealth distribution. Then, there is also a direct equivalence between measures of mixing and the magnitude of the standard measures of economic mobility. On the other hand, the opposite is not true. Wealth dynamics, are however, best modeled as non-mixing. Hence, measuring mobility using standard measures in a non-mixing system may lead to misleading conclusions about the extent of mobility across the whole distribution.