Biomedical subjects

Constantino Tsallis

Publications and source records attributed to Constantino Tsallis.

5 recordsLinked to original sources

PubMed2003

Constructing a statistical mechanics for Beck-Cohen superstatistics.

The basic aspects of both Boltzmann-Gibbs (BG) and nonextensive statistical mechanics can be seen through three different stages. First, the proposal of an entropic functional (S(BG)=-k Sigma(i)p(i)ln p(i) for the BG formalism) with the appropriate constraints (Sigma(i)p(i)=1 and Sigma(i)p(i)E(i)=U for the BG canonical ensemble). Second, through optimization, the equilibrium or stationary-state distribution (p(i)=e(-betaE(i))/Z(BG) with Z(BG)= Sigma(j)e(-betaE(j)) for BG). Third, the connection to thermodynamics (e.g., F(BG)=-(1/beta)ln Z(BG) and U(BG)=-(partial differential/partial differential beta)ln Z(BG)). Assuming temperature fluctuations, Beck and Cohen recently proposed a generalized Boltzmann factor B(E)= integral (infinity)(0)dbetaf(beta)e(-betaE). This corresponds to the second stage described above. In this paper, we solve the corresponding first stage, i.e., we present an entropic functional and its associated constraints which lead precisely to B(E). We illustrate with all six admissible examples given by Beck and Cohen.

Journal Article↗

PubMed2002

Metastability and weak mixing in classical long-range many-rotator systems.

We perform a molecular dynamical study of the isolated d=1 classical Hamiltonian H=1 / 2 summation operator (N)(i=1)L(2)(i)+ summation operator (i not equal j)[1-cos(theta(i)-theta(j))]/r(alpha)(ij); (alpha> or =0), known to exhibit a second order phase transition, being disordered for u identical with U/NN> or =u(c)(alpha,d) and ordered otherwise [U identical with total energy and N identical with (N(1-alpha/d)-alpha/d)/(1-alpha/d)]. We focus on the nonextensive case alpha/d< or =1 and observe that, for u infinity ), where, for all values of alpha/d, kappa(metastable) numerically coincides with one third of its value for u>u(c), hence decreases from 1/9 to zero when alpha/d increases from zero to unity, remaining zero thereafter. This simple connection between anomalies above and below the critical point reinforces the nonextensive universality scenario.

Journal Article↗

PubMed2002

Nonequilibrium probabilistic dynamics of the logistic map at the edge of chaos.

We consider nonequilibrium probabilistic dynamics in logisticlike maps x(t+1)=1-a|x(t)|(z), (z>1) at their chaos threshold: We first introduce many initial conditions within one among W>>1 intervals partitioning the phase space and focus on the unique value q(sen)<1 for which the entropic form S(q) identical with (1- summation operator Wp(q)(i))/(q-1) linearly increases with time. We then verify that S(q(sen))(t)-S(q(sen))( infinity ) vanishes like t(-1/[q(rel)(W)-1]) [q(rel)(W)>1]. We finally exhibit a new finite-size scaling, q(rel)( infinity )-q(rel)(W) proportional, variant W(-|q(sen)|). This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

Journal Article↗

PubMed2002

Border between regular and chaotic quantum dynamics.

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power-law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with [1+(q-1)(t/tau)2](1/(1-q)) (with the nonextensive entropic index q and tau depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.

Journal Article↗

PubMed2002

Asymmetric unimodal maps at the edge of chaos.

We numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps x(t+1)=1-a/x(t)/(z(i)) (i=1,2 correspond to x(t)>0 and x(t)<0, respectively, z(i)>1, 0<a< or =2, t=0,1,2,...) at the edge of chaos. We employ three distinct algorithms to characterize the power-law sensitivity to initial conditions at the edge of chaos, namely: direct measure of the divergence of initially nearby trajectories, the computation of the rate of increase of generalized non-extensive entropies S(q), and multi-fractal analysis. The first two methods provide consistent estimates for the exponent governing the power-law sensitivity. In addition to this, we verify that the multi-fractal analysis does not provide precise estimates of the singularity spectrum f(alpha), especially near its extremal points. Such feature prevents to perform a fine check of the accuracy of the scaling relation between f(alpha) and the entropic index q, thus restricting the applicability of the multi-fractal analysis for studying the sensitivity to initial conditions in this class of asymmetric maps.

Journal Article↗