Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-07-18
Chaos Solitons and Fractals 13 (2001) 471
Physics
Condensed Matter
Statistical Mechanics
7 pages, Latex, 9 figures included, talk presented at the Int. Conf. on "Classical and Quantum Complexity and Nonextensive The
Scientific paper
We 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.
Baranger Michel
Latora Vito
Rapisarda Andrea
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