1203.2707 (Nikos Kalogeropoulos)

Vanishing largest Lyapunov exponent and Tsallis entropy    [PDF]

Nikos Kalogeropoulos

We present a geometric, model-independent, argument that explains why the Tsallis entropy describes dynamical systems having vanishing largest Lyapunov exponent. We employ the Jacobi/geodesic deviation equation for an effective negative curvature Riemannian metric reflecting the Tsallis entropy composition property, whose solution gives the desired result. Extending the essential parts of the argument from Riemannian manifolds to CAT(k), k<0 spaces, we see that the conclusion remains valid in the case of interacting systems described by different entropic parameters. This conclusion is in agreement with all currently known results.

View original: http://arxiv.org/abs/1203.2707