1/fβ noise in a model for weak ergodicity breaking

Entropic Approach to the Detection of Crucial Events

In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1/f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.

Nonergodicity in nanoscale electrodes

The response of nanoscale electrodes displays deviations from conventional voltammetry theory that include a reduction in the limiting current and enhanced current fluctuations. We study the power spectra of these fluctuations in well characterized conical electrodes with radii between 2 and 10 nm. The fluctuations are found to display non-trivial power laws. We propose a model based on reversible adsorption of the redox species onto the nanoelectrode. This model is consistent with the non-stationary character of both the limiting current and the adsorption of molecules onto metal electrodes. Our model predicts the electrochemical reaction is nonergodic and sets fundamental limits on the sensitivity of uncoated nanoelectrodes.

Residence time statistics for N renewal processes

We present a study of residence time statistics for N renewal processes with a long tailed distribution of the waiting time. Such processes describe many nonequilibrium systems ranging from the intensity of N blinking quantum dots to the residence time of N Brownian particles. With numerical simulations and exact calculations, we show sharp transitions for a critical number of degrees of freedom N. In contrast to the expectation, the fluctuations in the limit of N→∞ are nontrivial. We briefly discuss how our approach can be used to detect nonergodic kinetics from the measurements of many blinking chromophores, without the need to reach the single molecule limit.