### Abstract

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".

Original language | English (US) |
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Pages (from-to) | 2924-2939 |

Number of pages | 16 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 392 |

Issue number | 13 |

DOIs | |

State | Published - Jul 1 2013 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

### Keywords

- Complex systems
- Decay-surge evolution
- Growth-collapse evolution
- Ito's stochastic differential equations
- Langevin's equation
- Reverse engineering

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## Cite this

*Physica A: Statistical Mechanics and its Applications*,

*392*(13), 2924-2939. https://doi.org/10.1016/j.physa.2013.02.021