On the Coupling of the Thermostatted Kinetic Theory with the Information Theory

Authors

Carlo Bianca, Laboratoire de Recherche en Eco-innovation Industrielle et Energetique, ´Ecole Superieure dIngenieurs en Genie ´Electrique, Productique et Management Industriel, Cergy-Pontoise 95092, FranceFollow

Author Country (or Countries)

France

Abstract

This paper deals with a further generalization of the continuous thermostatted kinetic theory for active particles. Specifically the interest focuses on the linking between the macroscopic data and the statistical evolution of the system. The connection between measurements and sources is established by defining an inverse problem based on the distribution vector function solution of the thermostatted kinetic framework. The inverse problem belongs to the class of ill-posed Volterra equations of the first kind considering that the number of sources can be greater of the number of measurements. The uniqueness of the solution is obtained by coupling the thermostatted kinetic theory with the information theory and more precisely with themaximum entropy principle of Jayne. Applications, which are discussed into the last section of the paper, refer to biological systems, vehicular traffic, crowds dynamics, and finance.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110623

Recommended Citation

Bianca, Carlo (2017) "On the Coupling of the Thermostatted Kinetic Theory with the Information Theory," Applied Mathematics & Information Sciences: Vol. 11: Iss. 6, Article 23.
DOI: http://dx.doi.org/10.18576/amis/110623
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss6/23