Quantity Of Entropy Research Articles

A generalized differential quadrature approach to the modelling of heat transfer in non-similar flow with nonlinear convection

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers.

A thermodynamical model of non-deterministic computation in cortical neural networks

Neuronal populations in the cerebral cortex engage in probabilistic coding, effectively encoding the state of the surrounding environment with high accuracy and extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron signaling outcomes as a thermodynamic process of non-deterministic computation. A mean field approach is used, with the trial Hamiltonian maximizing available free energy and minimizing the net quantity of entropy, compared with a reference Hamiltonian. Thermodynamic quantities are always conserved during the computation; free energy must be expended to produce information, and free energy is released during information compression, as correlations are identified between the encoding system and its surrounding environment. Due to the relationship between the Gibbs free energy equation and the Nernst equation, any increase in free energy is paired with a local decrease in membrane potential. As a result, this process of thermodynamic computation adjusts the likelihood of each neuron firing an action potential. This model shows that non-deterministic signaling outcomes can be achieved by noisy cortical neurons, through an energy-efficient computational process that involves optimally redistributing a Hamiltonian over some time evolution. Calculations demonstrate that the energy efficiency of the human brain is consistent with this model of non-deterministic computation, with net entropy production far too low to retain the assumptions of a classical system.

Entropy generation on EMHD transport of couple stress fluid with slip-dependent zeta potential under electrokinetic effects

This study theoretically explores the electroosmotic and electromagnetohydrodynamic (EMHD) transport of couple stress fluid in a microchannel subjected to an applied magnetic and electric field simultaneously to predict the flow dynamics, thermal transport, and entropy generation in a thermofluidic system with slip-dependent (SD) zeta potential. Solving the linearized Poisson-Boltzmann equation gives a closed-form solution for the slip-dependent (SD) electrical potential distribution established in the Electrical Double Layer (EDL). Using suitable boundary conditions and the SD zeta potential, analytical expressions for flow velocity, temperature, and entropy generation rate are determined. There are a variety of important parameters that have been considered, including the couple stress, slip length, Hartmann number, pressure gradient, and transverse electric field. The findings for each of these parameters are graphically displayed. After accounting for the SD zeta potential for the slip parameter and Hartmann number, the fluid velocity is shown to rise; however, the normalized velocity for the couple stress parameter exhibits the reverse trend owing to its strong resistive influence. It is noticed that with a higher Brinkman number, the magnitude value of the temperature is larger for SD zeta potential than for slip-independent (SI) zeta potential owing to an increase in viscous dissipation effect. The results reveal that the flow velocity and thermal energy distribution have a substantial effect on the quantity of entropy generated in the channel under SD zeta potential.

Analysis of Entropy Generation and Potential Inhibition in an Aeroengine System Environment

From a system perspective, the entropy generation of an aeroengine is directly related to the thermal efficiency when the Brayton cycle pressure ratio and maximum temperature remain constant. The lower the entropy generation of the engine is, the higher the thermal efficiency. However, the secondary air system of the engine generates a large quantity of entropy compared to the components of the main flow channel, because the irreversible losses of the internal flow and heat exchange between the air system components generate considerable entropy within the system. In this study, the theoretical method is used to build entropy generation model for different characteristics of air system components during the aerothermal process. In this basis, an integrated model of the whole engine is introduced to identify the key components for entropy generation in the system environment. The results show that the labyrinth at outlet of unloading cavity is recognized as the one that generates the most entropy in the entire aeroengine system, and the total entropy generation of the system is highly related to this component. Besides, in the system environment, entropy generation is the sum of the local entropy generated by the components and the total entropy generated by mixing of airflows in each component. High local entropy generated by components does not necessarily result in a high system entropy production, and vice versa. Therefore, when the minimum system entropy generation is the design goal, the most critical operations for entropy generation should be identified according to the corresponding sensitivity and parameter variation range, and the design should be improved accordingly.

Understanding entropy through a discussion of exergy

Entropy is an extremely important physical quantity in thermodynamics. However, students studying thermodynamics commonly find it difficult to understand entropy. In most thermodynamics textbooks, there is only a microscopic explanation of the physical meaning of entropy, with a lack of a macroscopic interpretation. This lack is far from sufficient for people who are more concerned about the macroscopic engineering applications of entropy. In this study, we comparatively analyse entropy and exergy to explain the macroscopic physical meaning of entropy based on the concept of exergy. That is, entropy is a measure of the unavailable energy of a system during reversible heat interaction with the environment. Based on this physical interpretation of entropy, we have answered three questions that students may raise when learning about the concept of entropy. In addition to theoretical derivation, we also try to use several examples from daily life to help readers better understand the macroscopic physical meaning of entropy. Finally, through a questionnaire survey, we learned about students’ evaluations and their understanding of an engineering thermodynamics course. We have also learned whether the students prefer entropy or exergy and the reasons for their preference, as well as what aspects regarding the contents and methods the students would prefer the lecturer to improve upon when teaching entropy and exergy. The results of this work can make it easier for students to understand the physical quantity of entropy. Additionally, the results of the questionnaire analysis can be of a certain reference value for the instructions of an engineering thermodynamics course.

Suppressing non-stationary random noise in microseismic data by using ensemble empirical mode decomposition and permutation entropy

Microseismic signal is inevitably mixed with non-stationary random noise in the process of acquisition, which is difficult to be separated from non-stationary random noise by using the traditional methods of linear filtering and spectrum analysis. Thus a suppressing method of non-stationary random noise is proposed. It firstly conducts the multi-scale decomposition of microseismic signal containing noises based on ensemble empirical mode decomposition (EEMD). Several components of Intrinsic Mode Functions (IMFs) are obtained and they are arranged in descending order according to their frequencies. In order to accurately identify the signals and noises in these IMF components and compare the normal microseismic signals with noises, the quantity of permutation entropy is introduced to describe the characteristics of normal microseismic signal. The threshold value of permutation entropy is used to extract the IMF components conforming to the characteristics of microseismic signal. These IMF components are reconstructed to suppress the noise. Through simulation and the test for the practical microseismic monitoring data, it is indicated that the method has a better treatment effect for non-stationary random noise in microseismic signal.

On the Smoothed Minimum Error Entropy Criterion

Recent studies suggest that the minimum error entropy (MEE) criterion can outperform the traditional mean square error criterion in supervised machine learning, especially in nonlinear and non-Gaussian situations. In practice, however, one has to estimate the error entropy from the samples since in general the analytical evaluation of error entropy is not possible. By the Parzen windowing approach, the estimated error entropy converges asymptotically to the entropy of the error plus an independent random variable whose probability density function (PDF) corresponds to the kernel function in the Parzen method. This quantity of entropy is called the smoothed error entropy, and the corresponding optimality criterion is named the smoothed MEE (SMEE) criterion. In this paper, we study theoretically the SMEE criterion in supervised machine learning where the learning machine is assumed to be nonparametric and universal. Some basic properties are presented. In particular, we show that when the smoothing factor is very small, the smoothed error entropy equals approximately the true error entropy plus a scaled version of the Fisher information of error. We also investigate how the smoothing factor affects the optimal solution. In some special situations, the optimal solution under the SMEE criterion does not change with increasing smoothing factor. In general cases, when the smoothing factor tends to infinity, minimizing the smoothed error entropy will be approximately equivalent to minimizing error variance, regardless of the conditional PDF and the kernel.

Measurement characteristics and properties of information entropy of heart rhythm diagrams

An entropy-based method of analysis consisting in a transition from probabilistic categories to the macro-parameters of the heart rhythm diagram is proposed for the heart rhythm diagram. These macro-parameters include the quantity of information, standard deviation, information entropy, and excess of entropy production. It is found that the heart rhythm diagram linearly accumulates a quantity of information. A distribution diagram of states and a distribution diagram of the scale of states are created. The system regulation–heart–adaptation includes mechanisms of control, regulation, and management.

Model-free derivations of the Tsallis factor: constant heat capacity derivation

The simple model-free derivations of the Boltzmann factor are extended by assuming the existence of an environment with a constant heat capacity in order to derive the Tsallis q-exponential factor, which reduces to the Boltzmann factor in the q→1 limit. It is shown that a constant of integration T c in the constant heat capacity derivation is related with the nonintensive generalized temperature T q , which is the thermal conjugate quantity of Tsallis' entropy S q .

Multiscale measures of equilibrium on finite dynamic systems

This article presents a new method for the study of the evolution of dynamic systems based on the notion of quantity of information. The system is divided into elementary cells and the quantity of information is studied with respect to the cell size. We have introduced an analogy between quantity of information and entropy, and defined the intrinsic entropy as the entropy of the whole system independent of the size of the cells. It is shown that the intrinsic entropy follows a Gaussian probability density function (PDF) and thereafter, the time needed by the system to reach equilibrium is a random variable. For a finite system, statistical analyses show that this entropy converges to a state of equilibrium and an algorithmic method is proposed to quantify the time needed to reach equilibrium for a given confidence interval level. A Monte-Carlo simulation of diffusion of A* atoms in A is then provided to illustrate the proposed simulation. It follows that the time to reach equilibrium for a constant error probability, t e, depends on the number, n, of elementary cells as: t e∝ n 2.22 ±0.06 . For an infinite system size ( n infinite), the intrinsic entropy obtained by statistical modelling is a pertinent characteristic number of the system at the equilibrium.

Testing procedures for spatially distributed flow models

Methods for testing, verifying, and validating predictive models of variably saturated groundwater flow are discussed. Specific procedures are introduced for measuring model complexity, assessing model consistency, and testing model validity. The discussion addresses numerical formulation, verification of internal consistency, benchmarking, groundtruth testing, performance measures, parameter estimation, hypothesis testing, and probabilistic induction. Verification of models includes tests of internal consistency and accuracy, like mass conservation and sensitivity to mesh size. Verification of codes also involves comparing results from the numerical model to analytical solutions, which are, however, limited in scope, and comparison with other numerical codes or ‘benchmarking’. These aspects are illustrated using available three-dimensional codes developed by the authors. Recognizing the diversity of spatially distributed modeling approaches, we also propose measures of model complexity and of the amount of information inherent in model predictions. One of these measures is the spatial degree of freedom, a function of material and boundary heterogeneities in the model. Another one is the quantity of information or entropy, which depends also on precision. Several aspects of ‘groundtruth’ model validation using data from laboratory and field tests are discussed. Logical inference is used to distinguish model validation from refutation. Recognizing that full validation is not possible in practice, we formulate performance criteria to define the ‘degree of validation’. Concepts and methods based on inductive calculus, Bayesian hypothesis testing, and maximum likelihood, are analyzed in some detail as alternative model validation strategies. Several examples of model testing are also discussed.

Universe creation, entropy, and extra dimensions

Gravitational bags contain a domain wall outside of which they look compact, but inside there is a solution in which, in certain circumstances, the extra dimensions explode. We show that it is energetically possible for a collapse of the domain wall to lead to the creation of a huge universe containing a large quantity of entropy. This can proceed via quantum tunneling through a “wormhole” region.

System physics: A uniform approach to the branches of classical physics

A systematic frame for the theory of classical physics is presented. The purpose of the modification in structure of the science is to economize the teaching, learning, and application of physics, and the communication with other disciplines. Isomorphic procedures applicable to the branches of physics and to other sciences are recommended. A system is defined as an imagined container; its contents of extensive (substancelike) quantities are used to describe the state of the system; balance equations account for the dynamic change in a system’s state through processes. The procedure, essentially a space integral formulation of macroscopic transport equations, is applied to physics by using the extensive quantity of entropy and the conserved extensive quantities of mass, energy, momentum, angular momentum, and electric charge. Examples are given from the areas of mechanics, electricity, and heat.

Entropy and Evolution

The conception of entropy came from the theoretical study of the steam-engine, and, neglecting refinements of mathematical treatment, can easily be illustrated. The motive power of the engine comes from the transformation of the heat generated by the combustion of the fuel. The mechanism transforms the kinetic energy of the molecules of heated steam into the kinetic energy of the parts of the engine. Consider a steamship under way: for a brief period of time this can be regarded as an automatic physical system. Some of the heat conveyed by the steam transforms directly into mechanical energy and some passes out into the ocean in the condenser water. We take the latter fraction: in the boiler there is a certain quantity, Q1, at a temperature of, say, 200°C, that is, 473° absolute, and its entropy is simply Q1/473° ab. The same quantity passes out into the ocean where its temperature falls to, say, 10°C, or 283° ab., and its entropy is now Q1/283° ab. Plainly the former quantity of entropy is less than the latter, so that in the transformation of heat into mechanical energy entropy has increased. The conception has been generalized so as to include all forms of energy and all physical transformations, and it can be shown that in all physical events that occur of themselves entropy increases. The conception includes these notions: (1) Available and unavailable energy; (2) greater or lesser improbability of the elements of the systems contemplated; and (3) the physical meanings of before and after.

The Entropy of Radiation

A QUANTITY of heat Q is transferred by radiation from a body the surface of which is at temperature T1 to a body the surface of which is at a lower temperature T2. From this cause alone the former body loses a quantity of entropy Q/T1, while the latter gains a quantity of entropy Q/T2. The net gain of entropy of the bodies arising from the transaction is Q(i/T2_ i/T1). Where and how does this gain take place? Vorlesungen über die Theorie der Wärrnestrahlung. By Dr. Max Planck. Pp. viii + 222. (Leipzig: Johann Ambrosius Barth, 1906.) Price 7 marks.

Localisation of Cerebral Functions

A QUANTITY of heat Q is transferred by radiation from a body the surface of which is at temperature T1 to a body the surface of which is at a lower temperature T2. From this cause alone the former body loses a quantity of entropy Q/T1, while the latter gains a quantity of entropy Q/T2. The net gain of entropy of the bodies arising from the transaction is Q(i/T2_ i/T1). Where and how does this gain take place? Vorlesungen uber die Theorie der Warrnestrahlung. By Dr. Max Planck. Pp. viii + 222. (Leipzig: Johann Ambrosius Barth, 1906.) Price 7 marks.