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A Convergence Theorem for the Nonequilibrium States in the Discrete Thermostatted Kinetic Theory

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  • Carlo Bianca

    (Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France
    Laboratoire de Recherche en Eco-innovation Industrielle et Energétique, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France)

  • Marco Menale

    (Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France
    Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, Viale Lincoln 5, I-81100 Caserta, Italy)

Abstract

The existence and reaching of nonequilibrium stationary states are important issues that need to be taken into account in the development of mathematical modeling frameworks for far off equilibrium complex systems. The main result of this paper is the rigorous proof that the solution of the discrete thermostatted kinetic model catches the stationary solutions as time goes to infinity. The approach towards nonequilibrium stationary states is ensured by the presence of a dissipative term (thermostat) that counterbalances the action of an external force field. The main result is obtained by employing the Discrete Fourier Transform (DFT).

Suggested Citation

  • Carlo Bianca & Marco Menale, 2019. "A Convergence Theorem for the Nonequilibrium States in the Discrete Thermostatted Kinetic Theory," Mathematics, MDPI, vol. 7(8), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:673-:d:252477
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    References listed on IDEAS

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    2. Máté Nagy & Zsuzsa Ákos & Dora Biro & Tamás Vicsek, 2010. "Hierarchical group dynamics in pigeon flocks," Nature, Nature, vol. 464(7290), pages 890-893, April.
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