From the kinetic theory of active particles to the modeling of social behaviors and politics

Abstract

Complexity, Kinetic theory, Nonlinearity, Social systems, Active particles,

Towards a mathematical theory of complex socio-economical systems by functional subsystems representation

“…Subsection 2.3 refers to welfare politics, focusing on the mechanisms according to which it is ruled by very general aspects of political economy. This issue is also dealt with in various papers [12], [13], [15], that apply methods of the discrete kinetic theory and stochastic games to social competition mathematical models. Methods derived from statistical mechanics are used to analyse political, economical, and social competitions phenomena [17], [18], [21], [29].…”

“…The mathematical approach takes advantage of the kinetic theory for active particles [7] already applied in various fields of life sciences, e.g. modelling multicellular systems [9], [11], and social behaviors of interacting individuals [12], [13], [15]. This mathematical theory describes the evolution of the probability distribution over the microscopic state, called activity, of several interacting entities called active particles.…”

Markov Chains and Kinetic Theory: A Possible Application to Socio-Economic Problems

“…In the past forty years, kinetic-theoretic models [1] (see Section 5 for more details) seem to be increasingly studied and applied in the research about the evolution of manyparticle systems. They seem to have delivered a particularly versatile, expressive, and effective tool to formulate suitable equations describing such evolution in stochastic terms (see [2][3][4][5][6][7][8][9][10][11], but these are only a few examples of the papers devoted to this kind of study: in each of them, the reader can find much more complete bibliographic references that are nevertheless far from being exhaustive), though other interesting and more effective models are available, e.g., the one based on Bayesian networks (see [12][13][14]). As pointed out in formal terms in [15], these equations are firmly based on the use of Markov Chains: in fact, transition matrices, which characterize these important stochastic processes, play a fundamental role in them, as they describe in stochastic terms the results of mutual interactions between the particles in the system.…”