Dynamic Entropies Research Articles

Information flow dynamics between cryptocurrency returns and electricity consumption: A comparative analysis of Bitcoin and Ethereum

Understanding energy consumption associated with cryptocurrency mining gained increasing attention, with the literature focusing mainly on Bitcoin. This study uses data from the two energy consumption indices, to estimate static and dynamic transfer entropies. The results provide a nuanced understanding of the bidirectional relationships and their implications. The dominant direction of information flow for Bitcoin is from electricity consumption to returns, while for Ethereum, it is from returns to electricity consumption, suggesting that Ethereum's returns significantly impact electricity consumption patterns. Results highlight the need for policies that integrate energy forecasting and environmental sustainability considerations and has significant implications for policymaking.

On some characterization results of -norm dynamic survival entropies

The information based on entropy of uncertainty associated with the residual life of a random variable is implemented in various fields, e.g., information theory, statistical physics, reliability theory, statistics, demography and economics, etc. In this paper, we propose two new -norm dynamic survival entropy (RNDSE) and -norm weighted dynamic survival entropy (RNWDSE) based on the survival function and some results on stochastic ordering are studied in detail. Further, we have investigated the bounds on RNDSE and RNWDSE in terms of failure rate function. In addition, some relationships between RNDSE, RNWDSE and failure function have also been well established. Finally, in order to illustrate the applications of RNDSE and RNWDSE, some useful distributions like exponential, Rayleigh, Weibull, Pareto, finite range distributions and one new distribution called T-exponential have been characterized.

Lightweight Integrated Design of PUF and TRNG Security Primitives Based on eFlash Memory in 55-nm CMOS

We present a lightweight, suitable for Internet of Things (IoT) devices, integrated design of physically unclonable function (PUF) and true random number generator (TRNG) based on embedded flash memory in 55-nm CMOS. In the proposed approach, the randomness in nonlinear ${I} - {V}$ characteristics and temporal current fluctuations of embedded flash memories are exploited to generate the dynamic and static entropies. Shared silicon in designing PUF and TRNG results in a very compact and energy-efficient topology. Experimental and simulation results demonstrate >10200 key space, 0.58-pJ/b energy efficiency for < 5% controllable bit error rate at 80 °C, up to 192.3-Mbps throughput, high Shannon entropy, and resiliency toward machine learning attacks. Accelerated aging measurements indicate stable physical unclonable function response after 900 min of baking at 85 °C.

Outlier Detection using Weighted Holoentropy with Hyperbolic Tangent Function

Numerous research works has been carried out in the literature to detect the outlier's a.k.a anomalies. Outlier detection is considered as a pre-processing step for locating those objects in a dataset that do not conform to well-defined notions of expected behaviour. In the proposed method, logistic sigmoid function related to hyperbolic tangent will be used as weightage function for finding the outlier data point(s). It can distribute the outlier data points effectively as compared with the reverse sigmoid function. The method is implemented with four phases. In the first phase, data is read out and dynamic entropy is calculated. In the second phase, probability and dynamic entropy computations using logistic sigmoid function related to hyperbolic tangent are performed. In the third phase, dynamic entropies are sorted and top N point is selected as outlier data point(s) and finally, the accuracy for correct outliers is computed for the proposed method.

Outlier detection using weighted holoentropy with hyperbolic tangent function

Numerous research works has been carried out in the literature to detect the outlier's a.k.a anomalies. Outlier detection is considered as a pre-processing step for locating those objects in a dataset that do not conform to well-defined notions of expected behaviour. In the proposed method, logistic sigmoid function related to hyperbolic tangent will be used as weightage function for finding the outlier data point(s). It can distribute the outlier data points effectively as compared with the reverse sigmoid function. The method is implemented with four phases. In the first phase, data is read out and dynamic entropy is calculated. In the second phase, probability and dynamic entropy computations using logistic sigmoid function related to hyperbolic tangent are performed. In the third phase, dynamic entropies are sorted and top N point is selected as outlier data point(s) and finally, the accuracy for correct outliers is computed for the proposed method.

Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family

For a system, which is observed at timet, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.

Some Results Based on a Version of the Generalized Dynamic Entropies

We propose new dynamic measures of uncertainty based on the notion of generalized dynamic entropy introduced in Di Crescenzo and Longobardi (2006). These can uniquely determine distribution functions in continuous and discrete cases, and the characterizations of some well-known distributions are provided. We also define some orderings and aging notions based on the generalized dynamic measures, and prove some of their properties, obtaining as corollaries results that have recently appeared in the literature.

Stochastic Comparisons of Residual Entropy of Order Statistics and Some Characterization Results

In this paper, we have presented some results for the residual and past entropies of order statistics. Results on the stochastic comparisons based on residual entropy of order statistics are presented. Characterization results for these dynamic entropies based on the sufficient condition for the uniqueness of the solution of an initial value problem have been considered.

Some Characterization Results Based on Dynamic Survival and Failure Entropies

In this paper, we develop some characterization results in terms of survival entropy of the first order statistic. In addition, we generalize the cumulative entropy recently proposed by Di Crescenzo and Logobardi (2009) to a new measure of information (called the failure entropy) and study some properties of it and its dynamic version. Furthermore, power distribution is characterized based on dynamic failure entropy.

Dynamic statistical information theory

In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy produc-tion rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel capacities reflecting the dynamic dissipation characteristics in the transmission processes, which change into their maximum—the present static mutual information and static channel capacity under the limit case where the proportion of channel length to informa-tion transmission rate approaches to zero. All these unified and rigorous theoretical for-mulas and results are derived from the evolution equations of dynamic information and dynamic entropy without adding any extra assumption. In this review, we give an overview on the above main ideas, methods and results, and discuss the similarity and difference between two kinds of dynamic statistical information theories.

Tracking a colloidal particle for the measurement of dynamic entropies

The paper describes the apparatus and measurement procedure for tracking long time trajectories of a single colloidal particle undergoing Brownian motion in water. The bulk motion obeys the Einstein–Stokes formulation, while sedimented motion is slowed by an additional drag known as the wall-drag effect. The sedimented particle trajectory is long enough to show diffusive motion spanning four decades in time. We describe the sample preparation, tracking routine, data-acquisition and noise. The experiment shows that Brownian motion exhibits a positive dynamic entropy consistent with microscopic chaos. The theoretical relevance of the experimental results is discussed.

Intraday patterns and local predictability of high-frequency financial time series

The structure of high-frequency time series of financial data taking the DAX future as an example is investigated with respect to the existence of local order on a time horizon of a few minutes. We will show that there might be special local situations where local order exists and where the predictability is considerably higher than average. We discretize the time series and investigate the continuation frequency of definite words of length n first. Besides higher order Shannon entropies and conditional entropies (dynamic entropies) which yield mean values of the uncertainty/predictability, we study the local values of the uncertainty/predictability and the distribution of these quantities. The local order significance is treated by means of surrogate sequences with identical short memory as the original data.

Local order, entropy and predictability of financial time series

We consider time series of financial data as the Dow Jones Index with respect to the existence of local order. The basic idea is that in spite of the high stochasticity in average there might be special local situations where there local order exist and the predictability is considerably higher than in average. In order to check this assumption we discretise the time series and investigate the frequency of the continuation of definite words of length n first. We prove the existence of relatively long-range correlations under special conditions. The higher order Shannon entropies and the conditional entropies (dynamical entropies) are calculated, characteristic fluctuations are found. Instead of the dynamic entropies which yield mean values of the uncertainty/predictability we finally investigate the local values of the uncertainty/predictability and the distribution of these quantities.

Prediction and entropy of nonlinear dynamical systems and symbolic sequences with LRO

Following Shannon we introduce higher order entropies and derive dynamic entropies. The nth order dynamic entropy (conditional entropy) is a measure of the uncertainty of the next state which follows after the observation of n foregoing states. The asymptotic behaviour of the dynamic entropies at large n is studied for several nonlinear model systems and for symbolic sequences with long-range order (LRO). For example we investigate 1D-maps, texts, DNA-strings and time series. It is shown that the existence of long correlations improves the possibility of predictions. Characteristic scaling laws for the higher order Shannon entropies and the conditional entropies are derived and a new interpolation formula is tested. Finally instead of the dynamic entropies which yield mean values of the uncertainty/predictability we investigate the local values of the uncertainty/predictability.

Markov processes, dynamic entropies and the statistical prediction of mesoscale weather regimes

Markov processes, dynamic entropies and the statistical prediction of mesoscale weather regimes

Markov processes, dynamic entropies and the statistical prediction of mesoscale weather regimes

The data pertaining to transitions between weather regimes grouped in 3 clusters are analyzed. Evidence that the dynamics of transitions between the regimes is not a first order Markov process is presented on the basis of the properties of residence time distributions. This conclusion is corroborated further by an entropy analysis revealing that the process is characterized by long range temporal correlations. Simple models of this behavior are developed and the repercussions on the problem of prediction are discussed.

Entropy and information in processes of self-organization: uncertainty and predictability

Abstract The mean uncertainties of probability distributions of discrete sets of events and those of dynamic sequences of events are investigated on the macroscopic and on the microscopic level. First one-time distributions are studied. The key point is the specification of the state space; the (coarse-grained) physical phase space leads to the thermodynamical entropy and the order parameter space to the informational entropy. In a similar way the uncertainty of the state after one step ahead in time, introduced by Shannon, McMillan and Khinchin, is related to the dynamic entropies studied by Kolmogorov and Sinai and to the gain of information. The non-equilibrium entropies and their relation to properties of attractors are discussed for several examples taken from physical and non-physical self-organization processes.

ON THE SEMANTICS OF ENTROPY MEASURES OF EMERGENT PHENOMENA

This paper is an attempt to perform some semantic analysis of the concept of “entropy” as it is used in both thermodynamic and nonthermodynamic contexts. We first consider the relation between thermodynamic entropy as a semantic concept, a measured quantity of real systems; and statistical entropy as a syntactic concept, a calculated quantity in formal systems. We then consider the use of entropy as a measure of different types of systems, the origin and identification of emergent levels in physical systems, and the ontological status of nonthermo dynamic entropies.

Star polymer diffusion in concentrated solutions: Dependence on functionality via the coupling model

AbstractThe coupling model is formulated in terms of the dynamic constraint entropy, Sc(t), and subsequently compared with measured tracer diffusion coefficients D for linear, 3‐arm star, and 12arm star polystyrenes in solutions of poly (vinyl methyl ether) (PVME) /o‐fluorotoluene. Inequalities between the dynamic constraint entropies, Scf and Scf′(t), respectively, for f‐arm and f′‐arm stars, enable us to explain the experimental observation that at constant arm molecular weight, the ratio Dstar/Dlinear decreases substantially with increasing concentration above the entanglement concentration for the PVME. This work indicates that not only the reptation model, but also the coupling model, can account for the experimental observation that in entangled solutions the mechanism for diffusion depends on diffusant architecture.