Related papers: Rare switching events in non-stationary systems
We investigate a family of multiple-stable processes that may exhibit either long-range or short-range dependence, depending on the parameters. There are two parameters for the processes, the memory parameter $\beta\in(0,1)$ and the…
Recent measurements of durations of non-equilibrium processes provide valuable information on microscopic mechanisms and energetics. Comprehensive theory for corresponding experiments so far is well developed for single-particle systems…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
In this paper, we introduce the concept of random time changes in dynamical systems. The sub- ordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of…
Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…
This thesis is devoted to the study of physical systems embedded within the field of non-equilibrium statistical mechanics. Specifically, the state of the systems of interest constitutes a stochastic process that can be externally driven by…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
A central concern across the natural sciences is a quantitative understanding of the mechanism governing rare transitions between two metastable states. Recent research has uncovered a fundamental equality between the time-reversal…
The transient behaviour of highly concentrated colloidal liquids and dynamically arrested states (glasses) under time-dependent shear is reviewed. This includes both theoretical and experimental studies and comprises the macroscopic…
Transition rates in continuously driven steady states were derived in [Evans R M L, 2005 J. Phys. A: Math. Gen. 38, 293] by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis…
Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…