Entropy production: evolution criteria, robustness and fractal dimension

J.A. Betancourt-Mar^a, M. Rodríguez-Ricard^b, R. Mansilla^c, G. Cocho^d,*, and J.M. Nieto-Villar^e,a

^a Mexican Institute of Complex Systems, Tamaulipas, México,

^b Departamento de Ecuaciones Diferenciales, Facultad de Matemática y Computación, Universidad de La Habana, La Habana 10400 Cuba.

^c Centro de Investigaciones Interdisciplinarias en Ciencias y Humanidades, Universidad Nacional Autónoma de México.

e Department of Chemical-Physics, M.V. Lomonosov Chemistry Division, Faculty of Chemistry, & H. Poincare Group of Complex Systems, Physics Faculty, University of Havana, Havana 10400 Cuba.

Received 13 October 2015;
accepted 4 January 2016

Abstract

It was proved through Rossler model, where the funnel case is more robust tan spiral chaos, the entropy production per unit time is a Lyapunov's function on the space of the control system parameters. It was established the conjecture of entropy production fractal dimension. The current theoretical framework will hopefully provide a better understanding of the relationship between thermodynamics and nonlinear dynamics and contribute to unify theses through complex systems theory.

Keywords: Irreversible thermodynamics; complex systems; fractal dimension.

PACS: 05.45.Pq; 05.45.Df; 05.70.Ln

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