The arrangements of particles and forces in granular materials have a complex organization
on multiple spatial scales that range from local structures to mesoscale and system-wide …

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

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 …

Granular materials are the most recurrent form of solid-state matter on Earth. They challenge
researchers and engineers in various fields not only because they occur with a broad variety …

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

In this work, we study the formal connections between the non-linear Fokker-Planck
Equation associated with the non-additive entropy and the Boltzmann Equation with the non …

Double‐scale numerical methods constitute an effective tool for simultaneously representing
the complex nature of geomaterials and treating real‐scale engineering problems such as a …

As a granular material is compressed, the particles and forces within the system arrange to
form complex and heterogeneous collective structures. Force chains are a prime example of …

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 …