Related papers: Fractional contact model in the continuum
Non-Markovian effects in an open-system dynamics are usually associated to information backflows from the environment to the system. However, the way these backflows manifest and how to detect them is unclear. A natural approach is to study…
In this work, with the help of fractional calculus, it is shown a time dependence of entropy more general than the well known Pesin relation is derived. Here the equiprobability postulate is not assumed, the system dynamic in the phase…
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in…
Inspired by analytic results obtained for a systematic expansion of the memory kernel in dissipative quantum mechanics, we propose a phenomenological procedure to incorporate non-markovian corrections to the Langevin dynamics of an order…
The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal…
Strong interaction with other particles or feedback from the medium on a Brownian particle entail memory effects in the effective dynamics. We discuss the extension of the fluctuation-dissipation theorem to nonequilibrium Langevin systems…
In this paper, we develop an encounter-based model of partial surface adsorption for fractional diffusion in a bounded domain. We take the probability of adsorption to depend on the amount of particle-surface contact time, as specified by a…
The logistic growth model is a classical framework for describing constrained growth phenomena, widely applied in areas such as population dynamics, epidemiology, and resource management. This study presents a generalized extension using…
We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The…
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular…
We introduce a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. Starting with a…
We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control…
We derive an extension to the quantum regression theorem which facilitates the calculation of two-time correlation functions and emission spectra for systems undergoing non-Markovian evolution. The derivation exploits projection operator…
We demonstrate the equivalence of a Non--Markovian evolution equation with a linear memory--coupling and a Fokker--Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…