Time evolution of thermodynamic entropy for conservative and dissipative chaotic maps

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dc.creatorBaranger, M.
dc.creatorLatora, V.
dc.creatorRapisarda, A.
dc.date2000-07-18
dc.date.accessioned2026-07-07T02:38:15Z
dc.date.available2026-07-07T02:38:15Z
dc.descriptionWe consider several low--dimensional chaotic maps started in far-from-equilibrium initial conditions and we study the process of relaxation to equilibrium. In the case of conservative maps the Boltzmann-Gibbs entropy S(t) increases linearly in time with a slope equal to the Kolmogorov-Sinai entropy rate. The same result is obtained also for a simple case of dissipative system, the logistic map, when considered in the chaotic regime. A very interesting results is found at the chaos threshold. In this case, the usual Boltzmann-Gibbs is not appropriate and in order to have a linear increase, as for the chaotic case, we need to use the generalized q-dependent Tsallis entropy $S_q(t)$ with a particular value of a q different from 1 (when q=1 the generalized entropy reduces to the Boltzmann-Gibbs). The entropic index q appears to be characteristic of the dynamical system.
dc.description7 pages, Latex, 9 figures included, talk presented at the Int. Conf. on "Classical and Quantum Complexity and Nonextensive Thermodynamics", Denton (Texas) April 3-6 2000, accepted fro publication in Chaos, solitons and fractals
dc.identifierhttps://arxiv.org/abs/cond-mat/0007302
dc.identifierhttp://arxiv.org/abs/cond-mat/0007302
dc.identifierChaos Solitons and Fractals 13 (2001) 471
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/16601
dc.subjectStatistical Mechanics
dc.subjectChaotic Dynamics
dc.titleTime evolution of thermodynamic entropy for conservative and dissipative chaotic maps
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