Entropy — Open Access Journal

We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs–von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature. Full article

A nonlinear random walk related to the porous medium equation (nonlinear Fokker–Planck equation) is investigated. This random walk is such that when the number of steps is sufficiently large, the probability of finding the walker in a certain position after taking a determined number of steps approximates to a q-Gaussian distribution ($G_{q,\beta }\left(x\right)\propto {[1-(1-q)\beta x^2]}^{1/(1-q)}$), which is a solution of the porous medium equation. This can be seen as a verification of a generalized central limit theorem where the attractor is a q-Gaussian distribution, reducing to the Gaussian one when the linearity is recovered ($q\to 1$). In addition, motivated by this random walk, a nonlinear Markov chain is suggested. Full article

Absorption chillers present opportunities to utilize sustainable fuels in the production of chilled water. An assessment of the steam driven absorption chiller at the University of Idaho, was performed to quantify the current exergy destruction rates. Measurements of external processes and flows were used to create a mathematical model. Using engineering equation solver to analyze and identify the major sources of exergy destruction within the chiller. It was determined that the absorber, generator and condenser are the largest contribution to the exergy destruction at 30%, 31% and 28% of the respectively. The exergetic efficiency is found to be 16% with a Coefficient of performance (COP) of 0.65. Impacts of weak solution concentration of lithium bromide on the exergy destruction rates were evaluated using parametric studies. The studies reveled an optimum concentration that could be obtained by increasing the weak solution concentration from 56% to 58.8% a net decrease in 0.4% of the exergy destruction caused by the absorption chiller can be obtained. The 2.8% increase in lithium-bromide concentration decreases the exergy destruction primarily within the absorber with a decrease of 5.1%. This increase in concentration is shown to also decrease the maximum cooling capacity by 3% and increase the exergy destruction of the generator by 4.9%. The study also shows that the increase in concentration will change the internal temperatures by 3 to 7 °C. Conversely, reducing the weak solution concentration results is also shown to increase the exergetic destruction rates while also potentially increasing the cooling capacity. Full article

We propose a novel feature selection method based on quadratic mutual information which has its roots in Cauchy–Schwarz divergence and Renyi entropy. The method uses the direct estimation of quadratic mutual information from data samples using Gaussian kernel functions, and can detect second order non-linear relations. Its main advantages are: (i) unified analysis of discrete and continuous data, excluding any discretization; and (ii) its parameter-free design. The effectiveness of the proposed method is demonstrated through an extensive comparison with mutual information feature selection (MIFS), minimum redundancy maximum relevance (MRMR), and joint mutual information (JMI) on classification and regression problem domains. The experiments show that proposed method performs comparably to the other methods when applied to classification problems, except it is considerably faster. In the case of regression, it compares favourably to the others, but is slower. Full article

Here, we consider the following inverse problem: Determination of an increasing continuous function $U(x)$ on an interval $[a,b]$ from the knowledge of the integrals $\int U(x)d{F}_{X_i}(x)={\pi }_i$ where the $X_i$ are random variables taking values on $[a,b]$ and ${\pi }_i$ are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when $U(x)$ is supposed to have a positive derivative, and it becomes a classical interpolation problem if the $X_i$ are deterministic. In some cases, e.g., in utility theory in economics, natural growth and convexity constraints are required on the function, which makes the inverse problem more interesting. Not only that, the data may be provided in intervals and/or measured up to an additive error. It is the purpose of this work to show how the standard method of maximum entropy, as well as the method of maximum entropy in the mean, provides an efficient method to deal with these problems. Full article

This paper formulates an unsupervised algorithm for symbolization of signal time series to capture the embedded dynamic behavior. The key idea is to convert time series of the digital signal into a string of (spatially discrete) symbols from which the embedded dynamic information can be extracted in an unsupervised manner (i.e., no requirement for labeling of time series). The main challenges here are: (1) definition of the symbol assignment for the time series; (2) identification of the partitioning segment locations in the signal space of time series; and (3) construction of probabilistic finite-state automata (PFSA) from the symbol strings that contain temporal patterns. The reported work addresses these challenges by maximizing the mutual information measures between symbol strings and PFSA states. The proposed symbolization method has been validated by numerical simulation as well as by experimentation in a laboratory environment. Performance of the proposed algorithm has been compared to that of two commonly used algorithms of time series partitioning. Full article

Transfer Entropy has been applied to experimental datasets to unveil causality between variables. In particular, its application to non-stationary systems has posed a great challenge due to restrictions on the sample size. Here, we have investigated the minimum sample size that produces a reliable causal inference. The methodology has been applied to two prototypical models: the linear model autoregressive-moving average and the non-linear logistic map. The relationship between the Transfer Entropy value and the sample size has been systematically examined. Additionally, we have shown the dependence of the reliable sample size and the strength of coupling between the variables. Our methodology offers a realistic lower bound for the sample size to produce a reliable outcome. Full article

The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In addition, Gram–Charlier-type (GCT) expansions, based on the aforementioned distributions and their orthogonal polynomials, are specified, and an operational criterion is provided to meet modelling requirements in a possibly severe kurtosis and skewness environment. The role played by entropy within the kurtosis ranges of GCT expansions is also examined. Full article

Terms related to gradients of scalar fields are introduced as scalar products into the formulation of entropy. A Lagrange density is then formulated by adding constraints based on known conservation laws. Applying the Lagrange formalism to the resulting Lagrange density leads to the Poisson equation of gravitation and also includes terms which are related to the curvature of space. The formalism further leads to terms possibly explaining nonlinear extensions known from modified Newtonian dynamics approaches. The article concludes with a short discussion of the presented methodology and provides an outlook on other phenomena which might be dealt with using this new approach. Full article

Turbulent flows are known to enhance turbulent transport. It has then even been suggested that turbulence is a state of maximum energy dissipation. In this paper, we re-examine critically this suggestion in light of several recent works around the Maximum Entropy Production principle (MEP) that has been used in several out-of-equilibrium systems. We provide a set of four different optimization principles, based on maximization of energy dissipation, entropy production, Kolmogorov–Sinai entropy and minimization of mixing time, and study the connection between these principles using simple out-of-equilibrium models describing mixing of a scalar quantity. We find that there is a chained-relationship between most probable stationary states of the system, and their ability to obey one of the four principles. This provides an empirical justification of the Maximum Entropy Production principle in this class of systems, including some turbulent flows, for special boundary conditions. Otherwise, we claim that the minimization of the mixing time would be a more appropriate principle. We stress that this principle might actually be limited to flows where symmetry or dynamics impose pure mixing of a quantity (like angular momentum, momentum or temperature). The claim that turbulence is a state of maximum energy dissipation, a quantity intimately related to entropy production, is therefore limited to special situations that nevertheless include classical systems such as shear flows, Rayleigh–Bénard convection and von Kármán flows, forced with constant velocity or temperature conditions. Full article

Multiscale cross-approximate entropy (MC-ApEn) between two different physiological signals could evaluate cardiovascular health in diabetes. Whether MC-ApEn analysis between two similar signals such as photoplethysmographic (PPG) pulse amplitudes of bilateral fingertips can reflect diabetes status is unknown. From a middle-to-old-aged population free of prior cardiovascular disease, we selected the unaffected (no type 2 diabetes, n = 36), the well-controlled diabetes (glycated hemoglobin (HbA1c) < 8%, n = 30), and the poorly- controlled diabetes (HbA1c ≥ 8%, n = 26) groups. MC-ApEn indexes were calculated from simultaneous consecutive 1500 PPG pulse amplitudes signals of bilateral index fingertips. The average of scale factors 1–5 (MC-ApEn_SS) and of scale factors 6–10 (MC-ApEn_LS) were defined as the small- and large-scales MC-ApEn, respectively. The MC-ApEn_LS index was highest in the unaffected, followed by the well-controlled diabetes, and then the poorly-controlled diabetes (0.70, 0.62, and 0.53; all paired p-values were <0.05); in contrast, the MC-ApEn_SS index did not differ between groups. Our findings suggested that the bilateral fingertips large-scale MC-ApEn_LS index of PPG pulse amplitudes might be able to evaluate the glycemic status and detect subtle vascular disease in type 2 diabetes. Full article

An abstract, quantitative theory which connects elements of information —key ingredients in the cognitive proces—is developed. Seemingly unrelated results are thereby unified. As an indication of this, consider results in classical probabilistic information theory involving information projections and so-called Pythagorean inequalities. This has a certain resemblance to classical results in geometry bearing Pythagoras’ name. By appealing to the abstract theory presented here, you have a common point of reference for these results. In fact, the new theory provides a general framework for the treatment of a multitude of global optimization problems across a range of disciplines such as geometry, statistics and statistical physics. Several applications are given, among them an “explanation” of Tsallis entropy is suggested. For this, as well as for the general development of the abstract underlying theory, emphasis is placed on interpretations and associated philosophical considerations. Technically, game theory is the key tool. Full article

In dilation or erosion processes, a shock filter is widely used in signal enhancing or image deburring. Traditionally, sign function is employed in shock filtering for reweighting of edge-detection in images and decides whether a pixel should dilate to the local maximum or evolve to the local minimum. Some researchers replace sign function with tanh function or arctan function, trying to change the evolution tracks of the pixels when filtering is in progress. However, analysis here reveals that only function replacement does usually not work. This paper revisits first shock filters and their modifications. Then, a fuzzy shock filter is proposed after a membership function in a shock filter model is adopted to adjust the evolve rate of image pixels. The proposed filter is a parameter tuning system, which unites several formulations of shock filters into one fuzzy framework. Experimental results show that the new filter is flexible and robust and can converge fast. Full article

To avoid structural failures it is of critical importance to detect, locate and quantify impact damage as soon as it occurs. This can be achieved by impact identification methodologies, which continuously monitor the structure, detecting, locating, and quantifying impacts as they occur. This article presents an improved impact identification algorithm that uses principal component analysis (PCA) to extract features from the monitored signals and an algorithm based on linear approximation with maximum entropy to estimate the impacts. The proposed methodology is validated with two experimental applications, which include an aluminum plate and an aluminum sandwich panel. The results are compared with those of other impact identification algorithms available in literature, demonstrating that the proposed method outperforms these algorithms. Full article

The characterisation of healthy ageing of the brain could help create a fingerprint of normal ageing that might assist in the early diagnosis of neurodegenerative conditions. This study examined changes in resting state magnetoencephalogram (MEG) permutation entropy due to age and gender in a sample of 220 healthy participants (98 males and 122 females, ages ranging between 7 and 84). Entropy was quantified using normalised permutation entropy and modified permutation entropy, with an embedding dimension of 5 and a lag of 1 as the input parameters for both algorithms. Effects of age were observed over the five regions of the brain, i.e., anterior, central, posterior, and left and right lateral, with the anterior and central regions containing the highest permutation entropy. Statistically significant differences due to age were observed in the different brain regions for both genders, with the evolutions described using the fitting of polynomial regressions. Nevertheless, no significant differences between the genders were observed across all ages. These results suggest that the evolution of entropy in the background brain activity, quantified with permutation entropy algorithms, might be considered an alternative illustration of a ‘nominal’ physiological rhythm. Full article

Ionogels are porous monoliths providing nanometer-scale confinement of an ionic liquid within an oxide network. Various dynamic parameters and the detailed nature of phase transitions were investigated by using a neutron scattering technique, giving smaller time and space scales compared to earlier results from other techniques. By investigating the nature of the hydrogen mean square displacement (local mobility), qualitative information on diffusion and different phase transitions were obtained. The results presented herein show similar short-time molecular dynamics between pristine ionic liquids and confined ionic liquids through residence time and diffusion coefficient values, thus, explaining in depth the good ionic conductivity of ionogels. Full article

The stochastic model of the Feynman–Smoluchowski ratchet is proposed and solved using generalization of the Fick–Jacobs theory. The theory fully captures nonlinear response of the ratchet to the difference of heat bath temperatures. The ratchet performance is discussed using the mean velocity, the average heat flow between the two heat reservoirs and the figure of merit, which quantifies energetic cost for attaining a certain mean velocity. Limits of the theory are tested comparing its predictions to numerics. We also demonstrate connection between the ratchet effect emerging in the model and rotations of the probability current and explain direction of the mean velocity using simple discrete analogue of the model. Full article

We consider two-receiver broadcast channels where each receiver may know a priori some of the messages requested by the other receiver as receiver message side information (RMSI). We devise a general approach to leverage RMSI in these channels. To this end, we first propose a pre-coding scheme considering the general message setup where each receiver requests both common and private messages and knows a priori part of the private message requested by the other receiver as RMSI. We then construct the transmission scheme of a two-receiver channel with RMSI by applying the proposed pre-coding scheme to the best transmission scheme for the channel without RMSI. To demonstrate the effectiveness of our approach, we apply our pre-coding scheme to three categories of the two-receiver discrete memoryless broadcast channel: (i) channel without state; (ii) channel with states known causally to the transmitter; and (iii) channel with states known non-causally to the transmitter. We then derive a unified inner bound for all three categories. We show that our inner bound is tight for some new cases in each of the three categories, as well as all cases whose capacity region was known previously. Full article

The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov–Curzon–Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero. Full article