Related papers: Transience in Dynamical Systems
Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
We continue development of the theory of Markov systems initiated in \cite{Wer1}. In this paper, we introduce fundamental Markov systems associated with random dynamical systems and show that the proof of the uniqueness and empiricalness of…
ONE of the main goals in the development of theory of chaotic dynamical system has been to make progress in understanding of turbulence. The attempts to related turbulence to chaotic motion got strong impetus from the celebrated paper by…
This note is a brief review of the analysis of long transients in dynamical systems. The problem of long transients arose in many disciplines, from physical and chemical kinetic to biology and even social sciences. Detailed analysis of…
Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides…
This contribution shortly outlines and reviews a theoretical and computational approach for a theory of change concerning systems where it is not possible to apply the laws of motion ab initio. The concept of meta-structure relates to the…
This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…
To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
In this paper, we consider the relationship between phase-type distributions and positive systems through practical examples. Phase-type distributions, commonly used in modelling dynamic systems, represent the temporal evolution of a set of…
Controlling phase transitions in quantum systems via coupling to reservoirs has been mostly studied for idealized memory-less environments under the so-called Markov approximation. Yet, most quantum materials and experiments in the solid…
Entropic Dynamics is a framework in which dynamical laws such as those that arise in physics are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by…
This paper presents description of time evolution of averages of Markov process in wide range of noise intensity. Exact expression of time scale of average evolution has been obtained. It has been demonstrated numerically that for purely…
Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted…