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Related papers: Entropy in the natural time-domain

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An efficient approach to the calculation of the $\epsilon$-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations…

chao-dyn · Physics 2009-10-31 M. Abel , L. Biferale , M. Cencini , M. Falcioni , D. Vergni , A. Vulpiani

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters,…

Data Analysis, Statistics and Probability · Physics 2016-01-20 Xiaofeng Liu , Aimin Jiang , Ning Xu , Jianru Xue

The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…

Statistical Mechanics · Physics 2009-11-10 W. T. Grandy

Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…

Statistical Mechanics · Physics 2015-05-18 Sumiyoshi Abe

1) Harmonic oscillations (HO) in numerous electroencephalograms (EEG) from different humans are introduced. 2) The probability density functions (PDF, p(X)) of the EEG voltages (X) are normal (Gauss) for OO whereas, the plots for the…

Biological Physics · Physics 2009-11-10 Caglar Tuncay

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…

Information Theory · Computer Science 2017-01-04 Günther Koliander , Georg Pichler , Erwin Riegler , Franz Hlawatsch

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of…

Condensed Matter · Physics 2015-06-24 Kazuo Fujikawa

Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…

Statistical Mechanics · Physics 2007-05-23 Roberto Luzzi , Áurea R. Vasconcellos , J. Galvão Ramos

The electroencephalographic (EEG) data intracerebrally recorded from 20 epileptic humans with different brain origins of focal epilepsies or types of seizures, ages and sexes are investigated (nearly 700 million data). Multi channel…

Biological Physics · Physics 2010-02-19 Caglar Tuncay

Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…

Probability · Mathematics 2025-03-21 Naveen Kumar , Ambesh Dixit , Vivek Vijay

We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…

Machine Learning · Computer Science 2016-06-09 David Darmon

Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…

Combinatorics · Mathematics 2021-10-22 John Stewart Fabila-Carrasco , Chao Tan , Javier Escudero

By making use of the concept of natural time, a simple model is proposed which exhibits the $1/f^a$ behavior with $a$ close to unity. The properties of the model are compared to those of the Seismic Electric Signals (SES) activities that…

Statistical Mechanics · Physics 2008-12-07 P. A. Varotsos , N. V. Sarlis , E. S. Skordas

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find…

Statistical Mechanics · Physics 2015-11-04 Marco Baiesi , Gianmaria Falasco

For stochastic non-equilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and…

Statistical Mechanics · Physics 2012-05-21 Udo Seifert

Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy…

Machine Learning · Computer Science 2023-05-19 Andrei Velichko , Maksim Belyaev , Yuriy Izotov , Murugappan Murugappan , Hanif Heidari

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…

Statistical Mechanics · Physics 2017-09-13 S. E. Marzen , J. P. Crutchfield

The celebrated Evans-Searles, respectively Gallavotti-Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper,…

Mathematical Physics · Physics 2025-08-05 T. Benoist , L. Bruneau , V. Jakšić , A. Panati , C. -A. Pillet

A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…

Quantum Physics · Physics 2011-11-14 Akimasa Miyake

We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…

Chemical Physics · Physics 2013-04-18 P. D. Gujrati