Search results for "entropy"
showing 10 items of 496 documents
Ab Initio Thermodynamics of Oxygen Vacancies and Zinc Interstitials in ZnO.
2015
ZnO is an important wide band gap semiconductor with potential application in various optoelectronic devices. In the current contribution, we explore the thermodynamics of oxygen vacancies and zinc interstitials in ZnO from first-principles phonon calculations. Formation enthalpies are evaluated using hybrid DFT calculations, and phonons are addressed using the PBE and the PBE+U functionals. The phonon contribution to the entropy is most dominant for oxygen vacancies, and their Gibbs formation energy increases when including phonons. Finally, inclusion of phonons decreases the Gibbs formation energy difference of the two defects and is therefore important when predicting their equilibrium c…
Probabilities, States, Statistics
2016
In this chapter we clarify some important notions which are relevant in a statistical theory of heat: The definitions of probability measure, and of thermodynamic states are illustrated, successively, by the classical Maxwell-Boltzmann statistics, by Fermi-Dirac statistics and by Bose-Einstein statistics. We discuss observables and their eigenvalue spectrum as well as entropy and we calculate these quantities for some examples. The chapter closes with a comparison of statistical descriptions of classical and quantum gases.
Theory of glass transition in spin glasses, orientational glasses and structural glasses
2008
Theoretical concepts about the glass transition are briefly reviewed, and the test of these ideas by Monte Carlo simulations of simple lattice models is described, with an emphasis on isotropic and anisotropic orientational glasses, and the bond fluctuation model of polymer melts. It is suggested that orientational glasses do have an equilibrium phase transition at zero temperature (in d = 3 dimensions!) only, in contrast to the Ising spin glass which orders at nonzero temperature. A diverging glass correlation length is identified that is responsible for the anomalous slowing down. For the Potts glass, the divergence seems to be exponential, implying that the model is at its lower critical…
Modelling of two step high spin⇌low spin transitions using the cluster variation method
1998
Abstract A thermodynamic description of high spin (HS)⇌low spin (LS) transition curves beyond the Bragg–Williams approximation is given using the Kikuchi cluster variation method (CVM). Transition curves of unusual behaviour (i.e. two step transition) are reproduced by short range interaction energies which are present in addition to long range elastic interaction between the spin changing molecules. The correlations in the distribution of the spin changing centers can be expressed analytically. They give rise to a reduced mixing entropy which was found experimentally in compounds with two step transitions.
Conditional Entropy-Based Evaluation of Information Dynamics in Physiological Systems
2014
We present a framework for quantifying the dynamics of information in coupled physiological systems based on the notion of conditional entropy (CondEn). First, we revisit some basic concepts of information dynamics, providing definitions of self entropy (SE), cross entropy (CE) and transfer entropy (TE) as measures of information storage and transfer in bivariate systems. We discuss also the generalization to multivariate systems, showing the importance of SE, CE and TE as relevant factors in the decomposition of the system predictive information. Then, we show how all these measures can be expressed in terms of CondEn, and devise accordingly a framework for their data-efficient estimation.…
Multiscale Information Storage of Linear Long-Range Correlated Stochastic Processes
2019
Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then …
Information dynamics of brain-heart physiological networks during sleep
2014
This study proposes an integrated approach, framed in the emerging fields of network physiology and information dynamics, for the quantitative analysis of brain-heart interaction networks during sleep. With this approach, the time series of cardiac vagal autonomic activity and brain wave activities measured respectively as the normalized high frequency component of heart rate variability and the EEG power in the δ, θ, Ï, and β bands, are considered as realizations of the stochastic processes describing the dynamics of the heart system and of different brain sub-systems. Entropy-based measures are exploited to quantify the predictive information carried by each (sub)system, and to dissec…
Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range co…
2017
Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of …
Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique
2010
We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected acc…
Entropy characteristics of heart rate wavelet multiscale components in epileptic children before and after seizures
2020
In this work, we analyze the information content of the multiple time scale components of heart rate variability (HRV) in children with focal epilepsy. HRV components are extracted from 30 pediatric patients, monitored 10 min and 10 s before and after focal epileptic seizures, using wavelet multiscale decomposition (with 5, 15, 30, 60, 120, 180 s time scale), and then characterized computing Entropy (E), permutation entropy (PE), conditional entropy (CE) and information storage (IS). Moving from preictal to postictal windows, we find statistically significant differences in the CE and IS values of HRV components at short time scales, which reflect autonomic imbalance and appear as potential…