# Emergence of Simple Characteristics for Heterogeneous Complex Social Agents

## Abstract

**:**

**20**, 329 (2019)] that some types of interactions among agents with many internal degrees of freedom may lead to a ‘simplification’ of agents, which are then effectively described by a small number of internal degrees of freedom. Here, we generalize the model to account for agent intrinsic heterogeneity. We find two different simplification regimes, one dominated by interactions, where agents become simple and identical as in the homogeneous model, and one where agents remain strongly heterogeneous although effectively with simple characteristics.

## 1. Introduction

## 2. Model

## 3. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Castellano, C.; Fortunato, S.; Loreto, V. Statistical physics of social dynamics. Rev. Mod. Phys.
**2009**, 81, 591. [Google Scholar] [CrossRef][Green Version] - Bouchaud, J.P.; Mézard, M.; Dalibard, J. (Eds.) Complex Systems; Elsevier: Amsterdam, The Netherlands, 2007. [Google Scholar]
- Barrat, A.; Barthélemy, M.; Vespignani, A. Dynamical Processes on Complex Networks; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar]
- Bouchaud, J.P. Crises and collective socio-economic phenomena: Simple models and challenges. J. Stat. Phys.
**2013**, 151, 567. [Google Scholar] [CrossRef][Green Version] - Anderson, P.W. More is different. Science
**1972**, 177, 393. [Google Scholar] [CrossRef] [PubMed][Green Version] - Chaikin, P.M.; Lubensky, T.C. Principles of Condensed Matter Physics; Cambridge University Press: Cambridge, UK, 1995. [Google Scholar]
- Le Bellac, M. Quantum and Statistical Field Theory; Oxford University Press: Hong Kong, China, 1992. [Google Scholar]
- Marchetti, M.C.; Joanny, J.F.; Ramaswamy, S.; Liverpool, T.B.; Prost, J.; Rao, M.; Simha, R.A. Hydrodynamics of soft active matter. Rev. Mod. Phys.
**2013**, 85, 1143. [Google Scholar] [CrossRef][Green Version] - De Gennes, P.G. Granular matter: A tentative view. Rev. Mod. Phys.
**1999**, 71, S374. [Google Scholar] [CrossRef] - Puglisi, A. Transport and Fluctuations in Granular Fluids; Springer: Berlin, Germany, 2015. [Google Scholar]
- Drossel, B. Biological evolution and statistical physics. Adv. Phys.
**2001**, 50, 209. [Google Scholar] [CrossRef] - Sella, G.; Hirsh, A.E. The application of statistical physics to evolutionary biology. Proc. Nat. Acad. Sci. USA
**2005**, 102, 9541. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sznajd-Weron, K.; Snajd, J. Opinion evolution in closed community. Int. J. Mod. Phys. C
**2000**, 11, 1157. [Google Scholar] [CrossRef][Green Version] - Deffuant, G.; Neau, D.; Amblard, F.; Weisbuch, G. Mixing beliefs among interacting agents. Adv. Complex Syst.
**2001**, 3, 87. [Google Scholar] [CrossRef] - Bertin, E.; Jensen, P. In social complex systems, the whole can be more or less than (the sum of) the parts. Comptes Rendus Phys.
**2019**, 20, 329. [Google Scholar] [CrossRef] - Latour, B.; Jensen, P.; Venturini, T.; Grauwin, S.; Boullier, D. The whole is always smaller than its parts, a digital test of Gabriel Tardes monads. Br. J. Sociol.
**2012**, 63, 590. [Google Scholar] [CrossRef] [PubMed] - Jensen, P. The politics of physicists’ social models. Comptes Rendus Phys.
**2019**, 20, 380. [Google Scholar] [CrossRef] - Anderson, S.; De Palma, A.; Thisse, J. Discrete Choice Theory of Product Differentiation; MIT Press: Cambridge, MA, USA, 1992. [Google Scholar]
- Phan, D.; Gordon, M.B.; Nadal, J.P. Social interactions in economic theory: An insight from statistical mechanics. In Cognitive Economics; Nadal, J.P., Bourgine, P., Eds.; Springer: Berlin, Germany, 2004; p. 335. [Google Scholar]
- Derrida, B. Random-energy model: Limit of a family of disordered models. Phys. Rev. Lett.
**1980**, 45, 79. [Google Scholar] [CrossRef] - Derrida, B. Random-energy model: An exactly solvable model of disordered systems. Phys. Rev. B
**1981**, 24, 2613. [Google Scholar] [CrossRef] - Bouchaud, J.P.; Mézard, M. Universality classes for extreme-value statistics. J. Phys. A Math. Gen.
**1997**, 30, 7997. [Google Scholar] [CrossRef][Green Version] - Angeletti, F.; Bertin, E.; Abry, P. On the existence of a glass transition in a Random Energy Model. J. Phys. A Math. Theor.
**2013**, 46, 315002. [Google Scholar] [CrossRef][Green Version] - Grauwin, S.; Bertin, E.; Lemoy, R.; Jensen, P. Competition between collective and individual dynamics. Proc. Natl. Acad. Sci. USA
**2009**, 106, 20622. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wu, F.Y. The Potts model. Rev. Mod. Phys.
**1982**, 54, 235. [Google Scholar] [CrossRef] - Blume, M.; Emery, V.J.; Griffiths, R.B. Ising model for the λ transition and phase separation in He
^{3}-He^{4}. Phys. Rev. A**1971**, 4, 1071. [Google Scholar] [CrossRef]

**Figure 1.**Phase diagram of the model in the $(k,T)$-plane (reduced coupling constant $k=K/M$ versus temperature), showing the three different regions separated by the critical line ${k}_{c}\left(T\right)$ (full line) and the ‘glass’ temperature ${T}_{\mathrm{g}}$ (dashed vertical line). For $k<{k}_{c}\left(T\right)$, agents configurations do not overlap ($q=0$), while for $k>{k}_{c}\left(T\right)$ agents become standardized by interactions ($q=1$). The $q=0$ area is subdivided into high- and low-temperature regions. For $T>{T}_{\mathrm{g}}$, agents may be in any of their internal configurations, while for $T<{T}_{\mathrm{g}}$, they are dynamically blocked in the few configurations with the highest intrinsic utility. In this latter case, agents appear simple but remain heterogeneous.

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**MDPI and ACS Style**

Bertin, E.
Emergence of Simple Characteristics for Heterogeneous Complex Social Agents. *Symmetry* **2020**, *12*, 1281.
https://doi.org/10.3390/sym12081281

**AMA Style**

Bertin E.
Emergence of Simple Characteristics for Heterogeneous Complex Social Agents. *Symmetry*. 2020; 12(8):1281.
https://doi.org/10.3390/sym12081281

**Chicago/Turabian Style**

Bertin, Eric.
2020. "Emergence of Simple Characteristics for Heterogeneous Complex Social Agents" *Symmetry* 12, no. 8: 1281.
https://doi.org/10.3390/sym12081281