Related papers: Correlation function and generalized master equati…
The relative ageing is an important notion which is useful to measure how a system ages relative to another one. Among all existing stochastic orders, there are two important orders describing the relative ageing of two systems, namely,…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
We consider the dynamics of a simple one dimensional model and we discuss the phenomenon of aging (i.e., the strong dependence of the dynamical correlation functions over the waiting time). Our model is the so-called random random walk, the…
Complex systems such as protein conformational fluctuations and supercooled liquids exhibit a long relaxation time and are considered to posses multiple relaxation times. We analytically obtain the exact correlation function for stochastic…
In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…
We study analytically the aging dynamics of the O(n) model in the large-n limit, with conserved and with non-conserved order parameter. While in the non-conserved dynamics, the autocorrelation function scales in the usual way C(t,tw) =…
The fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation. The transition rates are assumed to obey detailed balance also in the presence of a field. It is shown that in general the linear…
This paper generalizes a previously published differential equation that describes the relation between the age-specific incidence, remission, and mortality of a disease with its prevalence. The underlying model is a simple compartment…
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations…
We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and…
Aging is a prevalent phenomenon in physics, chemistry and many other fields. In this paper we consider the aging process of uncoupled Continuous Time Random Walk Limits (CTRWL) which are Levy processes time changed by the inverse stable…
We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form…
A method is presented that, when used in conjunction with single molecule experimental techniques, allows for the extraction of rates and mechanical properties of a biomolecule undergoing transitions between mechanically distinct states.…
We first review an approach that had been developed in the past years to introduce concepts of "bivariate ageing" for exchangeable lifetimes and to analyze mutual relations among stochastic dependence, univariate ageing, and bivariate…
Multivariate functional data that are cross-sectionally compositional data are attracting increasing interest in the statistical modeling literature, a major example being trajectories over time of compositions derived from cause-specific…
We demonstrate via several examples that a uniform drift velocity gives rise to anomalous aging, characterized by a specific form for the two-time correlation functions, in a variety of statistical-mechanical systems far from equilibrium.…
The concept of time correlation functions is a very convenient theoretical tool in describing relaxation processes in multiparticle systems because, on one hand, correlation functions are directly related to experimentally measured…
Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…
Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and L\'evy processes. By contrast, two-time occupation statistics, which…