Related papers: Entry and Return times distribution
Interpreting partial information collected from systems subject to noise is a key problem across scientific disciplines. Theoretical frameworks often focus on the dynamics of variables that result from coarse-graining the internal states of…
These lecture notes provide an elementary introduction, within the framework of finite quantum systems, to recent developments in the theory of entropic fluctuations.
The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the…
We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically,…
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer…
We show explicitly the entropy reduction from a detailed fluctuation theorem for the general stochastic system driven by nonequilibrium process under feedback control. The effect of interaction of the feedback controller with the system is…
This is a review on entropy in various fields of mathematics and science. Its scope is to convey a unified vision of the classical as well as some newer entropy notions to a broad audience with an intermediate background in dynamical…
We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of "weighted…
Feedback loops are known as a versatile tool for controlling transport in small systems, which usually have large intrinsic fluctuations. Here we investigate the control of a temporal correlation function, the waiting time distribution,…
We introduce a new concept of finite-time entropy which is a local version of the classical concept of metric entropy. Based on that, a finite-time version of Pesin's entropy formula and also an explicit formula of finite-time entropy for…
This chapter introduces evolutionary antifragility as the time-scale interaction characteristics of a natural dynamic system. It describes the benefit derived from input distribution unevenness, based on the emergent system dynamics and its…
In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…
This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
This paper is a short review on the application of continuos-time random walks to Econophysics in the last five years.
We review recent work on systems with multiple interacting-particles having the dynamical feature of stochastic resetting. The interplay of time scales related to inter-particle interactions and resetting leads to a rich behavior, both…
We show that under local detailed balance the expected entropy production rate is always bounded in terms of the dynamical activity. The activity refers to the time-symmetric contribution in the action functional for path-space…
Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to…
According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…
This is a survey on spectral theory of dynamical systems.