Entropy balance in distributed reversible Gray-Scott model

A practical way to calculate the entropy change in the distributed media composed of reversible Gray-Scott model is demonstrated. The entropy change is given as the sum of the entropy production and the divergence of entropy flow. The divergence of entropy is calculated based on the chemical potential of steady state. It becomes evident that: (i) the entropy change for the emergence of dissipative structures in the open system can be positive or negative, (ii) most of the entropy produced inside the system is thrown out to the environment when dissipative structures are developing, (iii) the entropy production and the divergence of entropy flow balance completely, when the system shows static steady states, (iv) the entropy change behaves as if it is the time derivative of the entropy production. Prior to these calculations of entropy balance, the features of emergent patterns in the two-dimensional system are examined in terms of entropy production solely. The results imply that the entropy production can be an index for us to discriminate spatial patterns, but is not a global thermodynamic potential for the evolution of dissipative structures.     

Stationary open systems: A brief review on contemporary theories on irreversibility

Open systems are very important in science and engineering for their applications and the analysis of the real word. At their steady state, two apparently opposed principles for their rate of entropy production have been proposed: the minimum entropy production rate and the maximum entropy production, useful in the analysis of dissipation and irreversibility of different processes in physics, chemistry, biology and engineering. Both principles involve an extremum of the rate of the entropy production at the steady state under non-equilibrium conditions. On the other hand, in engineering thermodynamics, dissipation and irreversibility are analyzed using the entropy generation, for which there exist two principle of extrema too, the minimum and the maximum principle. Finally, oppositions to the extrema principle have been developed too. In this paper, all these extrema principles will be analyzed in order to point out the relations among them and a synthesis useful in engineering applications, in physical and chemical process analysis and in biology and biotechnology will be proposed.     

Jamming III: Characterizing randomness via the entropy of jammed matter

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and this is shown to be difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to predict the entropy through the definition of a volume function that is dependent on the coordination number. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter, and elucidating the phase diagram for jammed granular matter. Analytical calculations are compared to numerical simulations using volume fluctuation analysis and graph theoretical methods, with reasonable agreement. The entropy of the jammed system reveals that random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits. Ensemble calculations show that the entropy vanishes at random close packing (RCP), while numerical simulations show that a finite entropy remains in the microscopic states at RCP. The notion of a negative compactivity, which explores states with volume fractions below those achievable by existing simulation protocols, is also explored, expanding the equations of state. The mesoscopic theory reproduces the simulations results in shape well, though a difference in magnitude implies that the entire entropy of the packing may not be captured by the methods presented herein. We discuss possible extensions to the present mesoscopic approach describing packings from random loose packing (RLP) to RCP to the ordered branch of the equation of state in an effort to understand the entropy of jammed matter in the full range of densities from RLP to face-centered cubic (FCC) packing.     

LETTER: The Nernst Theorem and the Entropy of the Reissner–Nordström Black Hole

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method on the background of the Reissner–Nordström black hole. We obtain the entropy of a scalar field is not only related to the location of an outer horizon but also is the function of the location of an inner horizon. In the approximation, the entropy is only proportional to the area of an outer horizon. The entropy expressed by location parameter of outer and inner horizon approaches zero, when the radiation temperature of a black hole approaches absolute zero. It satisfies the Nernst theorem.     

Information entropy of a dynamical system driven by quasimonochromatic noise

This paper shows the Fokker-Planck equation of a dynamical system driven by quasimonochromatic noise. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production for the system is calculated. The relationship between the properties of quasimonochromatic noise and dissipative parameter and their effects on entropy flux and entropy production are discussed.     

Entropy, entropy flux and entropy rate of granular materials

The aim of this work is to analyze the entropy, entropy flux and entropy rate of granular materials within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas that follows from the Boltzmann equation differs from the one of a simple fluid due to the presence of a term which can be identified as the entropy density rate. From the knowledge of a non-equilibrium distribution function-valid for processes closed to equilibrium-it is obtained that the entropy density rate is proportional to the internal energy density rate divided by the temperature, while the entropy flux is equal to the heat flux vector divided by the temperature. A thermodynamic theory of a granular material is also developed whose objective is the determination of the basic fields of mass density, momentum density and internal energy density. The constitutive laws are restricted by the principle of material frame indifference and by the entropy principle. Through the exploitation of the entropy principle with Lagrange multipliers, it is shown that the results obtained from the kinetic theory for granular gases concerning the entropy density rate and entropy flux are valid in general for processes close to equilibrium of granular materials, where linearized constitutive equations hold.     

Entropy production and thermal conductivity of a dilute gas

It is known that the thermal conductivity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by starting with two known entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. A remarkable feature of the new derivation is that it does not require the specification of the existence of the temperature gradient. The known result is reproduced in a similar form.     

Calculating Entropy of Plane Symmetry Black Hole via Generalized Uncertainty Relation

The generalized uncertainty relation is introduced to calculate entropy of the black hole. By using quantum statistical method, we directly obtain the partition function of Bose and Fermi field on the background of the plane symmetry black hole. Then we calculate the entropy of Bose and Fermi field on the background of black hole near the horizon of the black hole. In our calculation, we need not introduce cutoff. There are not the left out term and the divergent logarithmic term in the original brick-wall method. And it is obtained that the entropy of the black hole is proportional to the area of the horizon. The inherent contact between the entropy of black hole and the area of horizon is opened out. Further it is shown the entropy of black hole is entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect.     

图像局部熵用于小目标检测研究

分析了局部熵用于小目标检测时造成目标范围扩散等问题的原因,并提出了熵增长方法.该方法用于点目标检测可避免发生目标范围扩散现象.由于边缘纹理和点目标在熵增长处理过程中表现出截然相反的属性,故可避免边缘纹理对于小目标检测产生的严重干扰.该方法也可用于不受噪声干扰的边缘检测.针对相同信噪比目标在不同背景亮度中具有不同熵值和增长量的问题,提出用方差增长替代熵增长,使相同信噪比目标在不同背景亮度中表现出相同的增长量值,降低了后续目标分割的难度.试验表明,熵增长方法和方差增长方法能够有效检测1或2像素大小的点目标,并不受背景中边缘纹理的干扰.对算法的复杂度进行了分析,并提出采用双通道并行流水线方式实现工程化的设计思路.     

Entropy bound of horizons for accelerating,rotating and charged Plebanski–Demianski black hole

We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.     

Stationary solution of NLFP with coulombic potential

In a previous paper, Grassi (2012) [39], a new entropy form has been proposed for which it is possible to obtain a stationary solution of the Non-Linear Fokker–Planck equation (referred as NLFP) with coulombic-like potentials. In this paper we analyze the stationary solution of NLFP obtained by using pure coulombic potentials and we will use this solution to study an “atomic-like” system.     

Entropy production and viscosity of a dilute gas

It is known that the viscosity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by using two entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. The known result is reproduced in a similar form.     

Entropy and correlators in quantum field theory

It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.     

On the second law of thermodynamics: The significance of coarse-graining and the role of decoherence

We take up the question why the initial entropy in the universe was small, in the context of evolution of the entropy of a classical system. We note that coarse-graining is an important aspect of entropy evaluation which can reverse the direction of the increase in entropy, i.e., the direction of thermodynamic arrow of time. Then we investigate the role of decoherence in the selection of coarse-graining and explain how to compute entropy for a decohered classical system. Finally, we argue that the requirement of low initial entropy imposes constraints on the decoherence process.     

A geometrical measure for entropy changes

The geometrical approach to statistical mechanics is used to discuss changes in entropy upon sequential displacements of the state of the system. An interpretation of the angle between two states in terms of entropy differences is thereby provided. A particular result of note is that any state can be resolved into a state of maximal entropy (both states having the same expectation values for the constraints) and an orthogonal component. A cosine law for the general case is also derived.     

Entropy of MgO based on the Stacey equation of state

In the present communication we have modified the earlier calculations for the compression dependence of entropy of MgO using recent experimental data and more accurate equation of state. We have estimated the thermal expansivity with the help of the Anderson–Isaak equation at different compressions and selected temperatures up to the melting temperature of the solid. P–V relationship and compression dependence of isothermal bulk modulus are computed with the help of the Stacey equation of state. The results have been compared with those recommended by Cynn et al. [J. Phys. Chem. 99/19 (1995) 7813]. It is found that the entropy decreases with increasing compression along an isotherm.     

Universal canonical entropy for gravitating systems

The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by non-perturbative canonical quantum general relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonical entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has universal logarithmic corrections to the area law (from quantum space-time fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.     

On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

Entropy correlation distance method. The Euro introduction effect on the Consumer Price Index

The idea of entropy was introduced in thermodynamics, but it can be used in time series analysis. There are various ways to define and measure the entropy of a system. Here the so called Theil index, which is often used in economy and finance, is applied as it were an entropy measure. In this study the time series are remapped through the Theil index. Then the linear correlation coefficient between the remapped time series is evaluated as a function of time and time window size and the corresponding statistical distance is defined. The results are compared with the the usual correlation distance measure for the time series themselves. As an example this entropy correlation distance method (ECDM) is applied to several series, as those of the Consumer Price Index (CPI) in order to test some so called globalisation processes. Distance matrices are calculated in order to construct two network structures which are next analysed. The role of two different time scales introduced by the Theil index and a correlation coefficient is also discussed. The evolution of the mean distance between the most developed countries is presented and the globalisation periods of the prices discussed. It is finally shown that the evolution of mean distance between the most developed countries on several networks follows the process of introducing the European currency — the Euro. It is contrasted to the GDP based analysis. It is stressed that the entropy correlation distance measure is more suitable in detecting significant changes, like a globalisation process than the usual statistical (correlation based) measure.     

From Lotka to the entropy generation approach

The entropy approach to the evolution of open systems is analyzed, using Lotka’s principle as a starting point. A Lagrangian is sought after to develop an analytical method for the evaluation of the stationary states of open irreversible systems. The stationary conditions for open systems are first obtained on the basis of the entropy generation and its maximum principle, suggesting them as a link between the classical engineering thermodynamics approach and the more mathematical Lotka point of view.