The Boltzmann legacy revisited: kinetic models of social interactions

Abstract

The application of classical methods of statistical mechanics, originally developed by Ludwig Boltzmann in gas dynamics, to the description of social phenomena is a successful story that we try to outline in this paper. On one hand, it is nowadays a flourishing research line, which is more and more permeating different contexts such as the econophysics, sociophysics, biomathematics, transportation engineering to name just a few of them. On the other hand, it is a fascinating mathematical challenge, because it requires the interplay of various complementary expertises: modelling, model analysis, numerics. In this paper, we try to give a taste of all of this using the social phenomenon of opinion formation as a motivating example.

arXiv comment19 pages, 5 figures

References in corpus (6)

• Inelastically scattering particles and wealth distribution in an open economy
• Opinion dynamics: rise and fall of political parties
• Kinetic models for optimal control of wealth inequalities
• Uncertainty damping in kinetic traffic models by driver-assist controls
• Kinetic modelling of multiple interactions in socio-economic systems
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Cited by in corpus (5)

• Recent advances in opinion propagation dynamics: A 2020 Survey
• Opinion polarisation in social networks
• Macroscopic limits of non-local kinetic descriptions of vehicular traffic
• Network-based kinetic models: Emergence of a statistical description of the graph topology
• Approach to consensus in models of continuous-opinion dynamics: a study inspired by the physics of granular gases