Related papers: Decomposing Non-Markovian History Dependence
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…
Dynamics of information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for Markovian processes and study its behavior to observe information flow through the system. Examples of the…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We propose a procedure to fully reconstruct the time-dependent coefficients of convolutionless non-Markovian dissipative generators via a finite number of experimental measurements. By combining a tomography based approach with a proper…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
We construct a continuous-time, positively divisible non-Markovian process with memory of the initial state that satisfies the differential Chapman--Kolmogorov equation. In the stationary state, the correlation function exhibits exponential…
We propose a general framework to simulate stochastic trajectories with arbitrarily long memory dependence and efficiently evaluate large deviation functions associated to time-extensive observables. This extends the "cloning" procedure of…
Recently, a measure for the non-Markovian behavior of quantum processes in open systems has been developed which is based on the quantification of the flow of information between the open system and its environment [Phys. Rev. Lett. 103,…
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…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
Non-Markovian effects in open quantum system dynamics usually manifest backflow of information from the environment to the system, indicating complete-positive divisibility breaking of the dynamics. We provide a criterion for witnessing…
We introduce a notion of emergence for coarse-grained macroscopic variables associated with highly-multivariate microscopic dynamical processes, in the context of a coupled dynamical environment. Dynamical independence instantiates the…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
The visible dynamics of small-scale systems are strongly affected by unobservable degrees of freedom, which can belong either to external environments or internal subsystems and almost inevitably induce memory effects. Formally, such…
We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu-Paz-Zhang master equation of quantum…
The analysis of high-dimensional time series data has become increasingly important across a wide range of fields. Recently, a method for constructing the minimum information Markov kernel on finite state spaces was established. In this…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
We provide a characterization of memory effects in non-Markovian system-bath interactions from a quantum information perspective. More specifically, we establish sufficient conditions for which generalized measures of multipartite quantum,…