Random walk is a fundamental concept with applications ranging from quantum physics to
econometrics. Remarkably, one specific model of random walks appears to be ubiquitous …

Modern microscopic techniques following the stochastic motion of labelled tracer particles
have uncovered significant deviations from the laws of Brownian motion in a variety of …

The Boltzmann–Gibbs (BG) statistical mechanics constitutes one of the pillars of
contemporary theoretical physics. It is constructed upon the other pillars—classical …

We study the effect of resetting on diffusion in a logarithmic potential. In this model, a particle
diffusing in a potential U (x)= U 0 log| x| is reset, ie, taken back to its initial position, with a …

Definition The concept of entropy constitutes, together with energy, a cornerstone of
contemporary physics and related areas. It was originally introduced by Clausius in 1865 …

Abstract As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically
approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and …

Lévy flights are random walks in which the probability distribution of the step sizes is fat-
tailed. Lévy spatial diffusion has been observed for a collection of ultracold Rb 87 atoms and …

The brain is a complex system whose understanding enables potentially deeper
approaches to mental phenomena. Dynamics of wide classes of complex systems have …

This study investigates the interconnections between the traditional Fokker-Planck Equation
(FPE) and its fractal counterpart (FFPE), utilizing fractal derivatives. By examining the …

The pillars of contemporary theoretical physics are classical mechanics, Maxwell
electromagnetism, relativity, quantum mechanics, and Boltzmann–Gibbs (BG) statistical …