Partial equivalence of statistical ensembles and kinetic energy

The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore, the configurational microcanonical entropy is a smooth function, whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble. In the presence of a standard kinetic energy contribution, partial equivalence is removed and a nonanalyticity arises also microcanonically. Hence in contrast to the common belief, kinetic energy, even though a quadratic form in the momenta, has a nontrivial effect on the thermodynamic behaviour. As a by-product we present the microcanonical solution of the mean-field spherical model with kinetic energy for finite and infinite system sizes.     

Entropic information for travelling solitons in Lorentz and CPT breaking systems

In this work we group four research topics apparently disconnected, namely solitons, Lorentz symmetry breaking, supersymmetry, and entropy. Following a recent work (Gleiser and Stamatopoulos, 2012), we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang–Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are arbitrary. In this case, the CE selects the best value of the parameter in the model.     

Higher derivative correction to Kaluza–Klein black hole solution

We investigate the attractor mechanism in a Kaluza–Klein black hole solution in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black holes by using the effective potential approach as well as the entropy function formalism. We consider different higher derivative terms with a general coupling to the moduli field. For the R ² theory, we use an effective potential approach, looking for solutions which are analytic near the horizon and showing that they exist and enjoy attractor behavior. The attractor point is determined by extremization of the modified effective potential at the horizon. We study the effect of the general higher derivative corrections of R ⁿ terms. Using the entropy function we define the modified effective potential and we find the conditions to have the attractor solution. In particular for a single charged Kaluza–Klein black hole solution we show that a higher derivative correction dresses the singularity for an appropriate coupling, and we can find the attractor solution.     

Perturbation-induced compositional instability in epitaxial binary-alloy films

We examine the thermodynamic kernel that underpins dynamic models of instability in planar semiconductor alloys and explain how the energetics of perturbation produce decomposition in normally miscible alloys. By considering the relationship between epitaxial surface strain and the perturbation geometry, we show that amplification of the surface strain is the elastic cause of instability. We conclude by developing a nonlinear stability diagram for large-amplitude perturbations; configurational entropy terminates the growth of linearly unstable perturbations.     

Configurational entropy of systems with non-additive lateral interactions

The configurational entropy per site of a lattice gas model with non-additive interactions between adsorbed particles for square, triangular and honeycomb lattices is discussed in the present study. The model used here assumes that the energy which links a certain atom with any of its nearest-neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the canonical ensemble by following the algorithm of parallel tempering and the thermodynamic integration method the configurational entropy per site has been calculated. By analyzing the behavior of the configurational entropy per site, the different low-temperature-ordered phases are described. The dependency of the critical temperature of the system as a function of characteristic parameters of the model is established.     

Configurational electronic entropy and the phase diagram of mixed-valence oxides: the case of LixFePO4

We demonstrate that configurational electronic entropy, previously neglected, in ab initio thermodynamics of materials can qualitatively modify the finite-temperature phase stability of mixed-valence oxides. While transformations from low-T ordered or immiscible states are almost always driven by configurational disorder (i.e., random occupation of lattice sites by multiple species), in FePO4-LiFePO4 the formation of a solid solution is almost entirely driven by electronic rather than ionic configurational entropy. We argue that such an electronic entropic mechanism may be relevant to most other mixed-valence systems.     

Electric-field effect on shallow impurity ground state in nanowire superlattice

We have developed a variational formalism to analyze the effect of electric field on the donor ground state in a nanowire superlattice with cylindrical cross-section. The trial function is taken as a product of the free-electron ground state wave function with an envelope function that is a solution of a differential equation arising from the Schrödinger variational principle. We establish a close relationship between the donor ground state energy and density of charge induced by the unbound electron at the point of donor location. Also, we show that electric field applied along the crystal growth direction can easily shift the peak position of the free-electron density distribution from the central well toward one of the nanowire ends, providing a variation of the average electron-ion separation and a considerable alteration of the donor ground state energy.     

Interacting Entropy-Corrected Holographic Dark Energy and IR Cut-Off Length

In this paper we consider holographic dark energy model with corrected holographic energy density and show that this model may be equivalent to the modified Chaplygin gas model. Then we obtain relation between entropy corrected holographic dark energy model and scalar field models. We do these works by using choices of IR cut-off length proportional to the Hubble radius, the event horizon radius, the Ricci length, and the Granda-Oliveros length.     

Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties

Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius’ virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law’s evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students.     

Thermal contraction of carbon fullerenes and nanotubes

We perform molecular dynamics simulations to study shape changes of carbon fullerenes and nanotubes with increasing temperature. At moderate temperatures, these systems gain structural and vibrational entropy by exploring the configurational space at little energy cost. We find that the soft phonon modes, which couple most strongly to the shape, maintain the surface area of these hollow nanostructures. In nanotubes, the gain in entropy translates into a longitudinal contraction, which reaches a maximum at T approximately 800 K. Only at much higher temperatures do the anharmonicities in the vibration modes cause an overall expansion.     

纳柱阵列通道中生物分子等效淌度的宏观输运理论分析

各向异性生物分子或带电布朗粒子在周期性孔隙结构运动的分析在生物医学、水处理、环境工程等无数领域具有非常重要的意义. 本文基于宏观输运理论计算粒子在周期性微纳阵列结构中等效输运 参数, 预测分离结果. 首先通过引入构型熵及有效电荷等参数, 建立各向异性生物分子在纳米级受限环境下的等效布朗粒子模型, 然后应用宏观输运理论和数值方法计算分子的等效淌度. 以小分子DNA 片段在周期性纳柱阵列通道中电泳迁移为例, 证明当通道空隙接近或小于分子尺寸时, 熵受限对分子的等效迁移速度有重要的影响, 是实现生物分子分离的主要机理. 因为熵受限的作用随着外电场的增强而减低,所以在较低电场强度条件下, 分子淌度差别较大, 对应分离效果较佳. 关键词： 生物分子分离 构型熵 微纳阵列 宏观输运理论     

Reheating and entropy perturbations in fibre inflation

We study reheating in some one and two field realizations of fibre inflation.We find that reheating begins with a phase of preheating in which long wavelength fluctuation modes are excited.In two field models there is a danger that the parametric amplification of infrared fluctuations in the second scalar field-associated with an entropy mode-might induce an instability of the curvature fluctuations.We show that,at least in the models we consider,the entropy mode has a sufficiently large mass to prevent this instability.Hence,from the point of view of reheating the models we consider are well-behaved.     

Random Tilings of High Symmetry: I. Mean-Field Theory

We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our mean-field theory on an iterative tiling construction inspired by the work of de Bruijn. In addition to the entropy, we consider correlation functions, phason elasticity and the thermodynamic limit. Tilings of dimension other than two are considered briefly.     

Statistical thermodynamics of isolated rigid rod-like molecules near a surface

The configurational behaviour and thermodynamic properties of a dilute gas of rigid rod-like molecules in the vicinity of a macroscopic planar adsorption surface are investigated using statistical mechanics. The interaction energy between the surface and a rod-like molecule is determined as a function of both its molecular centre of mass separation R and its orientation relative to the surface. In calculating this interaction energy, each rod segment and molecule comprising the surface is assumed to interact through a Lennard-Jones pair potential. The average molecular order parameter is then determined as a function of R. We find that an isolated rod-like molecule tends to align nearly parallel to the surface for small separations. However, as R increases the order parameter first passes through a maximum then decays to zero as R ^-5 for large R. The configurational behaviour of an isolated rod-like molecule located between two parallel adsorption surfaces is also considered briefly. The surface spreading pressure, excess surface energy and entropy are also obtained for a dilute gas of rod-like molecules near a surface. We find that the extent of surface binding increases nearly exponentially with molecular length at constant temperature and surface density, and that the excess surface energy and entropy are essentially proportional to the molecular length.     

Configurational entropy of network-forming materials

We present a computationally efficient method to calculate the configurational entropy of network-forming materials. The method requires only the atomic coordinates and bonds of a single well-relaxed configuration. This is in contrast to the multiple simulations that are required for other methods to determine entropy, such as thermodynamic integration. We use our method to obtain the configurational entropy of well-relaxed networks of amorphous silicon and vitreous silica. For these materials we find configurational entropies of 0.93k(B) and 0.88k(B) per silicon atom, respectively.     

Generalizing Boltzmann Configurational Entropy to Surfaces,Point Patterns and Landscape Mosaics

Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds of landscape patterns, such as point patterns, surfaces, and patch mosaics. The goal of this paper is to evaluate if the direct application of the Boltzmann relation is fully generalizable to surfaces, point patterns, and landscape mosaics. I simulated surfaces and point patterns with a fractal neutral model to control their degree of aggregation. I used spatial permutation analysis to produce distributions of microstates and fit functions to predict the distributions of microstates and the shape of the entropy function. The results confirmed that the direct application of the Boltzmann relation is generalizable across surfaces, point patterns, and landscape mosaics, providing a useful general approach to calculating landscape entropy.     

Conformational temperature characterizing the folding of a protein

The time sequences of the molecular dynamics simulation for the folding process of a protein is analyzed with the inherent structure landscape which focuses on the configurational dynamics of the system. Time-dependent energy and entropy for inherent structures are introduced, and from these quantities a conformational temperature is defined. The conformational temperature follows the time evolution of a slow relaxation process and reaches the bath temperature when the system is equilibrated. We show that the nonequilibrium system is described by two temperatures, one for fast vibration and the other for slow configurational relaxation, while the equilibrium system is described by one temperature. The proposed formalism is applicable widely for systems with many metastable states.     

Probability distribution of inherent states in models of granular media and glasses

The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a “tap dynamics” analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new “thermodynamical” parameters, called “configurational temperatures” (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single “configurational temperature”. Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed. Received 19 March 2002 and Received in final form 14 June 2002     

Negative-temperature states and large-scale,long-lived vortices in two-dimensional turbulence

We study Onsager's theory of large, coherent vortices in turbulent flows in the approximation of the point-vortex model for two-dimensional Euler hydrodynamics. In the limit of a large number of point vortices with the energy perpair of vortices held fixed, we prove that the entropy defined from the microcanonical distribution as a function of the (pair-specific) energy has its maximum at a finite value and thereafter decreases, yielding the negative-temperature states predicted by Onsager. We furthermore show that the equilibrium vorticity distribution maximizes an appropriate entropy functional subject to the constraint of fixed energy, and, under regularity assumptions, obeys the Joyce-Montgomery mean-field equation. We also prove that, under appropriate conditions, the vorticity distribution is the same as that for the canonical distribution, a form of equivalence of ensembles. We establish a large-fluctuation theory for the microcanonical distributions, which is based on a level-3 large-deviations theory for exchangeable distributions. We discuss some implications of that property for the ergodicity requirements to justify Onsager's theory, and also the theoretical foundations of a recent extension to continuous vorticity fields by R. Robert and J. Miller. Although the theory of two-dimensional vortices is of primary interest, our proofs actually apply to a very general class of mean-field models with long-range interactions in arbitrary dimensions.