相关论文: Diffusion laws, information and action principle

The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light…

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion…

Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of…

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…

Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no…

The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this…

Starting with Arnold's pioneering work, the term "Arnold diffusion" has been used to describe the slow diffusion taking place in the space of the actions in Hamiltonian nonlinear dynamical systems with three or more degrees of freedom. The…

Using the methods of computer modeling this scientific paper studies the special features of diffusion of the particles subjected to the external periodic force in the crystal lattice. The particle motion is described by a Langevin…

Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful, but the methods are computationally expensive and typically…

The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…

Fluctuation theorems impose fundamental bounds in the statistics of the entropy production, with the second law of thermodynamics being the most famous. Using information theory, we quantify the information of entropy production and find an…

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction…

We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…

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…

We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we…

The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small…

In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…

Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…

We describe a method to extract force and diffusion parameters from single trajectories of Brownian particles based on the principle of maximum likelihood. The analysis is well-suited for out-of-equilibrium trajectories, even when a limited…