Generalized uncertainty principle and entropy of three-dimensional rotating acoustic black hole

Using the new equation of state density from the generalized uncertainty principle, we investigate statistics entropy of a 3-dimensional rotating acoustic black hole. When λ introduced in the generalized uncertainty principle takes a specific value, we obtain an area entropy and a correction term associated with the acoustic black hole. In this method, there does not exist any divergence and one needs not the small mass approximation in the original brick-wall model.     

Temperature field modeling during multi-modes CO2 laser irradiation of human enamel

We examine the temperature fields of human enamel [Yu D, Fox JL, Hsu J, Lynn Powell G, Higuchi WI. Computer simulation of surface temperature profiles during CO₂ laser irradiation of human enamel. Opt Eng 1993; 32(2)] during multi-modes CO₂ laser irradiation. For this we use the integral transform method as well as direct and inverse Laplace transform [Oane M, Sporea D. Temperature profiles modeling in IR optical components during high power laser irradiation. Infrared Phys Technol 2001; 42(1): 31–40; Oane M, Sporea D. Study of heat transfer in IR optical components during CO₂ laser irradiation. Proc SPIE 2001; 4430: 898–904; Oane M. Mathematical modeling of the thermal field distributions in solids under multiple laser irradiations. Proc SPIE 2003; 5227: 329–34; Oane M, Apostol I, Timcu A. Temperature field modeling in laser heated metals for laser cleaning of surfaces. Proc SPIE 2003; 5227: 323–8]. The enamel block is modeled as homogeneous cylinder in three dimensions. Results indicate that (i) the thermal field depends on multi-modes structure; (ii) heat transfer coefficient plays an important role in temperature distribution.     

A model of the holographic principle: Randomness and additional dimension

In recent years an idea has emerged that a system in a 3-dimensional space can be described from an information point of view by a system on its 2-dimensional boundary. This mysterious correspondence is called the Holographic Principle and has had profound effects in string theory and our perception of space-time. In this note we describe a purely mathematical model of the Holographic Principle using ideas from nonlinear dynamical systems theory. We show that a random map on the surface S² of a 3-dimensional open ball B has a natural counterpart in B, and the two maps acting in different dimensional spaces have the same entropy. We can reverse this construction if we start with a special 3-dimensional map in B called a skew product. The key idea is to use the randomness, as imbedded in the parameter of the 2-dimensional random map, to define a third dimension. The main result shows that if we start with an arbitrary dynamical system in B with entropy E we can construct a random map on S² whose entropy is arbitrarily close to E.     

A thermodynamic basis for the electronic properties of molten semiconductors: the role of electronic entropy

Abstract

The thermodynamic origin of a relation between features of the phase diagrams and the electronic properties of molten semiconductors is provided. Leveraging a quantitative connection between electronic properties and entropy, a criterion is derived to establish whether a system will retain its semiconducting properties in the molten phase. It is shown that electronic entropy is critical to the thermodynamics of molten semiconductor systems, driving key features of phase diagrams including, for example, miscibility gaps.     

The principle of the maximum entropy method

Abstract

The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of “entropy” is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.     

On the production of entropy within the concept of incomplete description of states

We calculate the linear response production of relevant entropy as defined recently by Balian. This quantity is — in contrast to the production of entropy defined in thermodynamics of irreversible processes — not determined by the linear transport coefficients alone but depends also on the susceptibilities with respect to the relevant observables. However, for systems satisfying a generalized ergodicity criterion the two expressions for the entropy production coincide.     

The maximum entropy principle as a consequence of the principle of Laplace

The maximum entropy principle states that the probability distribution which best represents our information is the one which maximizes the entropy with the given evidence as constraints. We prove that this principle is implied from the Laplace principle of equiprobabilities applied to the setS of allN-term sequences of results which are compatible with the given evidence. We generalize to the information gain method of Kullback.     

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.     

Verification of numerical simulation method for entropy generation of radiation heat transfer in semitransparent medium

The numerical simulation method of radiative entropy generation in participating media presented by Caldas and Semiao [Entropy generation through radiative transfer in participating media: analysis and numerical computation. JQSRT 2005;96:423-37] is extended to analyze the radiative entropy generation in the enclosures filled with semitransparent media. A discrete ordinates method is used to solve radiative transfer equation and radiative entropy generation. Two different examples are employed to verify the numerical simulation method of radiative entropy generation in the enclosure. Numerical results of dimensionless radiative entropy generation of enclosure are identical to that of entire thermodynamics analysis for the enclosure system. This numerical simulation method can be used in the entropy generation analysis of high-temperature systems such as boilers and furnaces, in which radiation is the dominant mode of heat transfer.     

On the connection of the formulas for entropy and stationary distribution

As is well known in statistical physics, the stationary distribution can be obtained by maximizing entropy. We show how one can reconstruct the formula for entropy knowing the formula for the stationary distribution. A general case is discussed and some concrete physical examples are considered.     

Black hole entropy and the modified uncertainty principle: A heuristic analysis

Recently Ali et al. (2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea here we calculate the quantum corrected value of a Schwarzschild black hole entropy and a Reissner-Nordström black hole with double horizon by utilizing the proposed generalized uncertainty principle. We find that the leading order correction goes with the square root of the horizon area contributing positively. We also find that the prefactor of the logarithmic contribution is negative and the value exactly matches with some earlier existing calculations. With the Reissner-Nordström black hole we see that this model-independent procedure is not only valid for single horizon spacetime but also valid for spacetimes with inner and outer horizons.     

Use and validity of principles of extremum of entropy production in the study of complex systems

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented.     

The influence of the ideal mixing entropy on concentration profiles and diffusion paths in ternary systems

The diffusion profiles and the reaction paths in ternary solid solutions are determined by both thermodynamics and kinetics. The matrix of the diffusion coefficient can be described as the product of the Hessian matrix for the thermodynamic influences and the Onsager matrix for kinetic influences.In this paper the interest is focused on the influence of the ideal part of the Hessian matrix, i.e. the ideal mixing entropy on interdiffusion. The ideal diffusion profiles are calculated by a computer simulation and they are compared with experimental results from the literature. These comparisons reveal that in most cases the qualitative shape of the diffusion profiles and of the reaction paths can be considered as caused by the ideal mixing entropy. Surprisingly, the shape of the diffusion profiles turns out to depend on the component that was chosen as the so-called solvent of the ternary mixture. This means that the ideal reaction paths do not show the triangular symmetry expected for an ideal ternary system. Especially, reaction paths between starting positions showing the same concentration of one of the three components do not run along straight lines.     

Generalized entropy optimization problems and the existence of their solutions

In the present study we have formulated a generalization of entropy optimization problems (GEOP), proposed sufficient conditions for the existence of solution. We have suggested also a new method based on a priori evaluations and Newton's methods for calculation of Langrange multipliers. Mentioned method allows calculating Langrange multipliers by starting from arbitrary initial point for Newton's approximations of constructed auxiliary equation. The solution of auxiliary equation is chosen as initial point for second constructed auxiliary equation. The recurring mentioned process for finite time leads to achieve an initial point for Newton's approximations of given equation and allows to find its unknown solution.     

Regional changes in the distribution of foreign aid: An entropy approach

Foreign aid contributes significantly to the income levels and economic viability of many developing countries. This paper investigates the dispersion in the distribution of foreign aid using the Theil entropy measure of inequality. Results show that the inequality (dispersion) of foreign aid has increased substantially in recent years. The increased inequality in the total distribution of aid has been due to both increases in the regional inequality of aid and increases in the average inequality of aid within each region. As a result, the distribution of aid is becoming less alike between regions and between countries within regions.     

Peculiarities in the behavior of the entropy diameter for molecular liquids as the reflection of molecular rotations and the excluded volume effects

The behavior of the diameter of the coexistence curve in terms of the entropy and the corresponding diameter are investigated. It is shown that the diameter of the coexistence curve in terms of the entropy is sensitive to the change in the character of the rotational motion of the molecule in liquid phase which is governed by the short range correlations. The model of the compressible effective volume is proposed to describe the phase coexistence both in terms of the density and the entropy.     

On the axiomatic approach to the maximum entropy principle of inference

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functionals, essentially of the form ∝ dx p(x)[p(x)/g(x)] ^s , for some real numbers, to be used for inductive inference and the commonly used form − ∝ dx p(x)ln[p(x)/g(x)] is only a particular case. The role of the prior densityg(x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.     

Statistical physics of human beings in games:Controlled experiments

It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings;making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system,thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.     

Positivity of entropy production in the presence of a random thermostat

We study nonequilibrium statistical mechanics in the presence of a thermostat acting by random forces, and propose a formula for the rate of entropy productione() in a state . When is a natural nonequilibrium steady state we show thate()0, and sometimes we can provee()>0.