On the diffusive nature of entropy flow in infinite systems: Remarks to a paper by Guo-Papanicolau-Varadhan

The hydrodynamic behaviour of interacting diffusion processes is investigated by means of entropy (free energy) arguments. The methods of [13] are simplified and extended to infinite systems including a case of anharmonic oscillators in a degenerate thermal noise. Following [14, 15] and [3–5] we derive a priori bounds for the rate of entropy production in finite volumes as the size of the whole system is infinitely extended. The flow of entropy through the boundary is controlled in much the same way as energy flow in diffusive systems [4].This work was supported in part by the Hungarian National Foundation for Scientific Research Grant 1815, NSF Grant DMR 86-12369, and by the Institut des Hautes Etudes Scientifiques     

Entanglement entropy in Abelian gauge theories

The definition of geometric entanglement entropy associated with some region in space is discussed for the case of gauge theories. It is argued that since in gauge theories elementary excitations look like loops (closed electric strings) rather than points (particles), the boundaries of the regions should also carry some nonzero entropy. This entropy counts the number of strings which cross these boundaries. Explicit calculations of such entropy are carried out in the limits of infinitely strong and weak couplings of three- and four-dimensional Z _N gauge theories. In three dimensions we find that the entropy is a constant which does not depend on the region, while in four dimensions the familiar area law for the entropy is recovered.     

Why finite mathematics is the most fundamental and ultimate quantum theory will be based on finite mathematics

Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of mathematics are discussed.     

A Generalized Measure of Cumulative Residual Entropy

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy, such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of this generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss a generating function approach, using which we derive different entropy measures. We provide residual and cumulative versions of Sharma–Taneja–Mittal entropy and obtain them as special cases this generalized measure of entropy. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.     

Debye screening for jellium and other Coulomb systems

Debye screening is proven for a large class of classical Coulomb gases at low densities. Among the models treated are jellium systems (where particles interact with a fixed background charge), systems with arbitrarily dilute fractional charges, and systems where the charges are not integrally related. The interaction potentials of the corresponding sine-Gordon models may have no symmetry and can have infinitely many stationary points which are degenerate or nearly degenerate in energy.Junior Fellow, Harvard University Society of Fellows. Supported in part by the National Science Foundation under Grant No. PHY79-16812     

Entropic measure for localized energy configurations: Kinks,bounces, and bubbles

We construct a configurational entropy measure in functional space. We apply it to several nonlinear scalar field models featuring solutions with spatially-localized energy, including solitons and bounces in one spatial dimension, and critical bubbles in three spatial dimensions, typical of first-order phase transitions. Such field models are of widespread interest in many areas of physics, from high energy and cosmology to condensed matter. Using a variational approach, we show that the higher the energy of a trial function that approximates the actual solution, the higher its relative configurational entropy, defined as the absolute difference between the configurational entropy of the actual solution and of the trial function. Furthermore, we show that when different trial functions have degenerate energies, the configurational entropy can be used to select the best fit to the actual solution. The configurational entropy relates the dynamical and informational content of physical models with localized energy configurations.     

Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes

The matter collineation classifications of Kantowski-Sachs, Bianchi types I and III space times are studied according to their degenerate and non-degenerate energy-momentum tensor. When the energy-momentum tensor is degenerate, it is shown that the matter collineations are similar to the Ricci collineations with different constraint equations. Solving the constraint equations we obtain some cosmological models in this case. Interestingly, we have also found the case where the energy-momentum tensor is degenerate but the group of matter collineations is finite dimensional. When the energy-momentum tensor is non-degenerate, the group of matter collineations is finite-dimensional and they admit either four which coincides with isometry group or ten matter collineations in which four ones are isometries and the remaining ones are proper.     

Entanglement dynamics and quasiprobability distribution for the degenerate Raman process

In this paper, we consider the model which consists of a degenerate Raman process involving two degenerate Rydberg energy levels of an atom interacting with a single-mode cavity field. The influence of the atomic coherence on the von Neumann entropy of the atom and the atomic inversion is investigated. It is shown that the atomic coherence decreases the amount of atom-field entanglement. It is also found that the collapse and revival times are independent of the atomic coherence, while the amplitude of the revivals is sensitive to this coherence. Moreover, the Q function and the entropy squeezing of the field are examined. Some new conclusions can be obtained.     

Full spectrum of the Rabi model

It is shown that in the Rabi model, for an integer value of the spectral parameter x, in addition to the finite number of the classical Judd states there exist infinitely many possible eigenstates. These eigenstates exist if the parameters of the problem are zeros of a certain transcendental function; in other words, there are infinitely many possible choices of parameters for which integer x belongs to the spectrum. Moreover, it is shown that the classical Judd eigenstates appear as degenerate cases of the confluent Heun function.     

Multiple phase transitions in the generalized Curie-Weiss model

The generalized Curie-Weiss model is an extension of the classical Curie-Weiss model in which the quadratic interaction function of the mean spin value is replaced by a more general interaction function. It is shown that the generalized Curie-Weiss model can have a sequence of phase transitions at different critical temperatures. Both first-order and second-order phase transitions can occur, and explicit criteria for the two types are given. Three examples of generalized Curie-Weiss models are worked out in detail, including one example with infinitely many phase transitions. A number of results are derived using large-deviation techniques.     

Sensitive Response of the Quantum Entropies to Jaynes-Cummings Model in Presence of a Second Harmonic Generation

The behavior of a modified Jaynes-Cummings Hamiltonian model (two-level atom in interaction with an electromagnetic field) in the presence of degenerate parametric amplification is introduced. We have examined two different cases, one when the field frequency ω is not equal to the splitting photon frequency ε for which the off-resonance case is considered. In the second case we have taken each frequencies to be equal (ω = ε) and considered the system to be at exact resonance. The wave function for both cases is obtained and the result used to calculate the density matrix from which we manage to discuss the field entropy as well as the phase entropy. It is shown that the system is sensitive to any change in the splitting photon frequency ε.     

变耦合系数的简并拉曼耦合J-C模型中场熵的演化

研究了考虑耦合系数随时间线形变化的简并拉曼耦合J-C模型中场熵随时间演化特性,分析了耦合系数变化的快慢和不同的初始光场对场熵的影响。结果表明:(1)无论光场初始态如何,场熵均呈周期性演化,平均光子数n-的增加并不改变场熵演化周期的大小;(2)初始光场统计性质的不同对最大场熵值和最大场熵值变化的幅度产生较大的影响;(3)线形调制使场熵呈现的完美周期性振荡遭到破坏。当原子-场耦合系数变化缓慢时,原子进入统计混合态的速度被减缓;而当原子-场耦合系数变化较快时,则不仅使场熵演化曲线的振荡周期逐渐减小、振荡频率越来越快,而且使原子与场退纠缠的时刻增多。     

Application of the Lifshitz theory to poor conductors

The Lifshitz formula for dispersive forces is generalized to the materials, which cannot be described with the local dielectric response. The principal nonlocality of poor conductors is related to the finite screening length of the penetrating field and collisional relaxation; at low temperatures the role of collisions plays the Landau damping. Spatial dispersion makes the theory self-consistent. Our predictions are compared with the recent experiment. It is demonstrated that at low temperatures Casimir-Lifshitz entropy disappears as T in the case of degenerate plasma and as T2 for the nondegenerate one.     

Can we understand (and model) aqueous solutions without any long range electrostatic interactions?

A computer simulation experiment has been conducted to study the extent to which long range Coulombic interactions are indispensable when modelling aqueous solutions of electrolytes. A simple molecular model, which accounts explicitly for the molecular structure of water but which does not incorporate any long range Coulombic interactions is employed. The solvent is primitive water (EPM5-4 model) and the solute molecules are hard spheres interacting with the interaction sites of the water molecule by means of either repulsive (like-charge interaction) or attractive (unlike-charge interaction) short range triangular-well tails. The structural changes (hydrophobic ordering, structure breaking, and structure enhancement) which take place in an infinitely dilute solution upon ‘charging’ the solute were studied, in terms of the correlation functions and of the orientational distribution functions and of the average binding energy of the water molecules around the solute in terms of their dependence on the solute-water oxygen distance. The main thermodynamic property reflecting these changes is the residual entropy. This quantity is found to exhibit an asymmetric double maximum, in agreement with the findings for a realistic counterpart of this simple model that employs long range Coulombic interactions.     

Phase separation of highly dissymmetric binary ionic mixtures

We study the phase separation of binary ionic mixtures involving two species of classical point ions in a rigid uniform neutralizing background of degenerate electrons. The thermodynamic properties of the ionic fluid are calculated on the basis of the HNC integral equation for the three partial pair distribution functions. We develop a systematic technique which allows the properties of mixtures of arbitrary composition to be expressed in terms of infinitely dilute solutions. Phase diagrams and critical parameters are determined for 12 different binary systems involving ionic charge ratios between 2 and 8. The dependence of the critical temperature on the ionic charges, on the pressure and an ionic quantum corrections is examined in detail.     

Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.     

Magnetic transitions in strong coupling expansions for nearly degenerate states

A strong coupling expansion for a two‐band Hubbard model on two sites with nearly degenerate states is considered. A comparative analysis is performed for different schemes of perturbation theory which are applicable to systems with nearly degenerate states. A fourth order approach which builds on a four‐dimensional low‐energy subspace with nearly degenerate states captures accurately the transition from an antiferromagnetic to a ferromagnetic ground state at large on‐site Coulomb interaction.     

Perturbation theory of von Neumann entropy

In quantum information theory, von Neumann entropy plays an important role; it is related to quantum channel capacities. Only for a few states can one obtain their entropies. In a continuous variable system, numeric evaluation of entropy is not easy due to infinite dimensions. We develop the perturbation theory for systematically calculating von Neumann entropy of a non-degenerate system as well as a degenerate system.     

Ricci Collineations in Perfect Fluid Bianchi V Spacetime

The Bianchi V spacetimes with perfect-fluid matter are classified according to their Ricci collineations. We have found that in the degenerate case there are infinitely many Ricci collineations whereas a subcase gives a finite number of Ricci collineations which are five. In the non-degenerate case the group of Ricci collineations is finite, i.e. four or five or six or seven. Also, all results obtained satisfy the energy conditions.     

Current Distribution in a Gyrotropic Microstrip Structure when Excited by a Plane Electromagnetic Wave

The problem of the distribution of the surface current density in a gyrotropic microstrip structure representing an infinitely thin ideally conducting strip arranged on a substrate of a chiral metamaterial metallized from one side and excited by a plane wave is reduced to a one-dimensional singular integral equation with a Cauchy singularity. The complex current distributions along the strip conductor are presented for different types of substrate and the wave-incidence angles.