On the physical interpretation of statistical data from black-box systems

• We study the physical interpretation of statistical data from complex black-box systems.
• Five Markov-based reverse-engineering methodologies are established and exemplified.
• Three methodologies are based on Langevin, geometric Langevin, and diffusion dynamics.
• Two methodologies are based on growth-collapse and decay-surge dynamics.
• The methodologies are applied to the distribution of wealth and income in human societies.

In this paper we explore the physical interpretation of statistical data collected from complex black-box systems. Given the output statistics of a black-box system, and considering a class of relevant Markov dynamics which are physically meaningful, we reverse-engineer the Markov dynamics to obtain an equilibrium distribution that coincides with the output statistics observed. This reverse-engineering scheme provides us with a conceptual physical interpretation of the black-box system investigated. Five specific reverse-engineering methodologies are developed, based on the following dynamics: Langevin, geometric Langevin, diffusion, growth-collapse, and decay-surge. In turn, these methodologies yield physical interpretations of the black-box system in terms of conceptual intrinsic forces, temperatures, and instabilities. The application of these methodologies is exemplified in the context of the distribution of wealth and income in human societies, which are outputs of the complex black-box system called “the economy”.