Related papers: The Stochastic Nature of Complexity Evolution in t…
Unlike the classical exponential relaxation law, the widely prevailing universal law with its fractional power-law dependence of susceptibility on frequency cannot be explained in the framework of any intuitively simple physical concept.…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
The dynamics of a degree of freedom associated to an axial vector in contact with a heat bath is decribed by means of a probability distribution function obeying a Fokker-Planck equation. The equation is derived by using mesoscopic…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…
In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
Dielectric relaxation has been investigated within the framework of a modified mean field theory, in which the dielectric response of an arbitrary condensed matter system to the applied electric field is assumed to consist of two parts, a…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
The theory of SOC, and related avalanche dynamics, is proposed as the origin of the ubiquitous nonexponential relaxation observed in complex systems. Introducing some scaling laws and relations we have obtained that the normalized…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
In chaotic reaction-diffusion systems with two degrees of freedom, the modes governing the exponential relaxation to the thermodynamic equilibrium present a fractal structure which can be characterized by a Hausdorff dimension. For long…
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…
The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of…
We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…