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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

We discuss the concept of entropy applied to the infinite-N Kuramoto model and derive an expression for its time derivative. The time derivative of the entropy functional is shown to depend on the synchronization order parameter in a very…

Pattern Formation and Solitons · Physics 2015-07-08 Anders Nordenfelt

The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional…

Chaotic Dynamics · Physics 2013-05-29 Arul Lakshminarayan , Steven Tomsovic

Uncertainty is an important feature of dynamic systems, and entropy has been widely used to measure this attribute. In this Letter, we prove that state aggregation and decomposition can decrease and increase the entropy, respectively, of…

Information Theory · Computer Science 2022-05-18 Lirong Cui , Xiangchen Li , Narayanaswamy Balakrishnan

A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space $(X,\mu)$. These have…

Dynamical Systems · Mathematics 2015-08-25 Tim Austin

The entropy production rate is central to the study of non-equilibrium systems. This parameter is closely connected to violation of time-reversal symmetry, energy consumption, efficiency, and other properties of interest; in short, it…

Statistical Mechanics · Physics 2026-05-28 John W. Biddle

In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as…

Data Analysis, Statistics and Probability · Physics 2022-06-07 Inmaculada Leyva , Johann Martinez , Cristina Masoller , Osvaldo A. Rosso , Massimiliano Zanin

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are…

The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…

Statistical Mechanics · Physics 2013-05-30 Ian J. Ford , Richard E. Spinney

The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is…

Statistical Mechanics · Physics 2024-12-17 Pedro E. Harunari , Carlos E. Fiore , Andre C. Barato

Isolating slower dynamics from fast fluctuations has proven remarkably powerful, but how do we proceed from partial observations of dynamical systems for which we lack underlying equations? Here, we construct maximally-predictive states by…

Biological Physics · Physics 2023-02-28 Antonio Carlos Costa , Tosif Ahamed , David Jordan , Greg Stephens

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…

Data Analysis, Statistics and Probability · Physics 2013-11-12 A. N. Gorban , P. A. Gorban , G. Judge

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

Statistical Mechanics · Physics 2024-05-09 Samuel D. Gelman , Guy Cohen

In this paper, we show that, under some technical assumptions, the Kolmogorov-Sinai entropy and the permutation entropy are equal for one-dimensional maps if there exists a countable partition of the domain of definition into intervals such…

Dynamical Systems · Mathematics 2018-08-03 Tim Gutjahr , Karsten Keller

We propose a robust and computationally efficient algorithm to generically construct first return maps of dynamical systems from time series without the need for embedding. Typically, a first return map is constructed using a heuristic…

Dynamical Systems · Mathematics 2023-05-24 Zahra Shahriari , Shannon Dee Algar , David M. Walker , Michael Small

Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…

Quantum Physics · Physics 2007-05-23 Elias P. Gyftopoulos

Entropy in nonequilibrium statistical mechanics is investigated theoretically so as to extend the well-established equilibrium framework to open nonequilibrium systems. We first derive a microscopic expression of nonequilibrium entropy for…

Statistical Mechanics · Physics 2007-06-13 Takafumi Kita

Kolmogorov-Sinai entropy is an invariant of measure-preserving actions of the group of integers that is central to classification theory. There are two recently developed invariants, sofic entropy and Rokhlin entropy, that generalize…

Dynamical Systems · Mathematics 2020-11-25 Lewis Bowen

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this…

Dynamical Systems · Mathematics 2009-11-11 Claudio Bonanno , Pierre Collet

We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…

General Relativity and Quantum Cosmology · Physics 2025-07-16 Tanisha Joshi