Description: This article discusses aging rejuvenation with fractional derivatives. Abstract: We discuss a dynamic procedure that makes a fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index μ in the interval 2<μ<3, yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, o, is given by o=3-μ. A brand new system is characterized by the degree o=μ-2. If the system is prepared at time -tₐ<0 and the observation begins at time t=0, we derive the following scenario. For times 0<t«tₐ the system is satisfactorily described by the fractional derivative with o=3-μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t⪢tₐ yields o=μ-2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.

Description: This article discusses anomalous diffusion and environment-induced quantum decoherence. Abstract: We study the anomalous diffusion resulting from the standard map in the so-called accelerating state, and we observe that it is determined by unusually large times of sojourn of the classical trajectories in the fractal region at the border between the chaotic sea and the acceleration island. The quantum-mechanical breakdown of this property implies a coherence among so slightly different values of momentum as to become much more robust against environment fluctuations than the quantum localization corresponding to normal diffusion.

Description: This article discusses linear response and 1/f optimal information transport. Article: Nonergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. The authors show that it is possible to go beyond the "death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating nonergodic renewal processes, by taking as stimulus a similar nonergodic process. The ideal condition of 1/f noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

Description: This article discusses brain, music, and non-Poisson renewal processes. Abstract: In this paper we show that both music composition and brain function, as revealed by the electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion the authors process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. The the authors show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a technique of statistical analysis recently developed by the authors' group, the aging experiment (AE). First, the authors find that in both cases the distances between two consecutive events are described by nonexponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities ψ(t) are well fitted by stretched exponentials [ψ(t) ∝ exp (-(yt)a), with 0.5<a<1.] The second step rests on the adoption of AE, which shows that these are renewal processes. The authors show that the stretched exponential, due to its renewal character, is the emerging tip of an iceberg, whose underwater part has slow ...

Description: This article discusses chaos and thermal conductivity. Abstract: We argue that the condition of local thermal equilibrium realized several years ago by Rich and Visscher [Phys. Rev. B 11, 2164 (1975)] through a process of mathematical convergence can be obtained dynamically by adopting the prescription of a recent paper [M. Bianucci, R. Mannella, B.J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)]. This should contribute to shedding light on the still unsolved problem fo the microscopic derivation of the heat Fourier law.