Related papers: Entropies in case of continuous time
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
We review the behaviour of the Gibbs' and conditional entropies in deterministic and stochastic systems and continue to a formulation appropriate for a stochastically perturbed system with delayed dynamics. The underlying question driving…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
The deterministic notions of capacity and entropy are studied in the context of communication and storage of information using square-integrable, bandlimited signals subject to perturbation. The $(\epsilon,\delta)$-capacity, that extends…
Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which…
We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic…
We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
The maximum entropy ansatz, as it is often invoked in the context of time-series analysis, suggests the selection of a power spectrum which is consistent with autocorrelation data and corresponds to a random process least predictable from…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…