Information,Entropy, Life,and the Universe

In 2015, I wrote a book with the same title as this article. The book’s subtitle is: “What we know and what we do not know.” On the book’s dedication page, I wrote: “This book is dedicated to readers of popular science books who are baffled, perplexed, puzzled, astonished, confused, and discombobulated by reading about Information, Entropy, Life and the Universe.” In the first part of this article, I will present the definitions of two central concepts: the “Shannon measure of information” (SMI), in Information Theory, and “Entropy”, in Thermodynamics. Following these definitions, I will discuss the framework of their applicability. In the second part of the article, I will examine the question of whether living systems and the entire universe are, or are not within the framework of applicability of the concepts of SMI and Entropy. I will show that much of the confusion that exists in the literature arises because of people’s ignorance about the framework of applicability of these concepts.     

Quantum Theory of the Classical: Einselection,Envariance, Quantum Darwinism and Extantons

Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer’s records. However, our “let quantum be quantum” approach poses questions absent in Bohr’s Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply “too relative”, and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born’s rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the ‘quantum theory of the classical’ one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born’s rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.     

On the Solvability of the Discrete s(x,·)-Laplacian Problems on Simple,Connected, Undirected,Weighted, and Finite Graphs

We use the finite dimensional monotonicity methods in order to investigate problems connected with the discrete -Laplacian on simple, connected, undirected, weighted, and finite graphs with nonlinearities given in a non-potential form. Positive solutions are also considered.     

Pressure-induced phase transitions in the ZrXY (X= Si,Ge, Sn;Y= S,Se, Te) family compounds

Pressure is an effective and clean way to modify the electronic structures of materials, cause structural phase transitions and even induce the emergence of superconductivity. Here, we predicted several new phases of the ZrXY family at high pressures using the crystal structures search method together with first-principle calculations. In particular, the ZrGeS compound undergoes an isosymmetric phase transition from P4/nmm-I to P4/nmm-II at approximately 82 GPa. Electronic band structures show that all the high-pressure phases are metallic. Among these new structures, P4/nmm-II ZrGeS and P4/mmm ZrGeSe can be quenched to ambient pressure with superconducting critical temperatures of approximately 8.1 K and 8.0 K, respectively. Our study provides a way to tune the structure, electronic properties, and superconducting behavior of topological materials through pressure.     

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum,Fragmentation, and the Variance of Entropy

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.     

Viscosity,heat conductivity,and Prandtl number effects in the Rayleigh–Taylor Instability

The two-dimensional Rayleigh–Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosity and heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainly achieved by inhibiting the development of the Kelvin–Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilibrium manifestations and the degree of correlation between the nonuniformity and the nonequilibrium strength in the complex flow are systematically investigated.     

Theoretical study of the [Si,C, P,O] potential energy surface

The structures, energetics, spectroscopies and stability of the doublet [Si, C, P, O] radical are explored at the density functional theory and ab initio levels. Eighteen isomers connected by 22 interconversion transition states are located at the DFT/B3LYP/6-311G(d) level. The structures of the kinetically stable isomers and the relevant transition states are further optimized at the QCISD/6-311G(d) level followed by CCSD(T)/6-311 + G(2df) single-point energy calculations. At the QCISD/6-311G(d) level, the lowest-lying isomer is the cyclic O-cCSiP 8 (0.0 kcal/mol) with considerable kinetic stability of 22.0 kcal/mol. In addition, two bent isomers OSiCP 1 (7.3 kcal/mol) and SiCPO 3 (34.7 kcal/mol) also possess considerable kinetic stability (more than 10.0 kcal/mol). As a result, three isomers 1, 3 and 8 are predicted to be possible candidates for future experimental and astrophysical detection. The bonding nature of the three isomers is analysed. The calculated results are compared with those of the analogous radical [Si, C, N, O]. Implications in the laboratory and interstellar space are also discussed. The predicted structures and spectroscopic properties are expected to be informative for the identification of [Si, C, P, O] in the laboratory and space.     

Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.     

Analytical Solutions,Moments, and Their Asymptotic Behaviors for the Time-Space Fractional Cable Equation

Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.     

Assessing,Testing and Estimating the Amount of Fine-Tuning by Means of Active Information

A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function f quantifies specificity for each possible outcome x of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target as intended than by chance. The distribution of a random outcome X of the algorithm involves a parameter θ that quantifies how much background information has been infused. A simple choice of this parameter is to use θf in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis–Hastings type of Markov chain, which makes it possible to compute their active information under the equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters θ are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming.     

Dosimetric properties of the newly developed KLT-300 (LiF:Mg,Cu,Na,Si) TL detector

The dosimetric properties of the newly developed KLT-300 (KAERI LiF:Mg,Cu,Na,Si TL detector) in KAERI (Korea Atomic Energy Research Institute) were investigated. The sensitivity of the TL detector was about 30 times higher than that of the TLD-100 by light integration. In the study of the dose linearity of the detector, the dose response was very linear up to 10 Gy and a sublinear response was observed at higher doses. The energy response of the detector was studied for photon energies from 20 to 662 keV. The results show that a maximum response of 1.004 at 53 keV and a minimum response of 0.825 at 20 keV were observed. The reproducibility study for the TL detector was also carried out. The coefficients of variation for each detector separately did not exceed 0.016, and for all the 10 detectors collectively it was 0.0054. IEC Standard requires that the coefficient of variation shall not exceed 0.075. So, the reproducibility of this new TL detector sufficiently satisfied the IEC requirements. A detection threshold of the detector was investigated and found to be 70 nGy by Harshaw 4500 TLD Reader.     

Inference,Prediction, & Entropy-Rate Estimation of Continuous-Time,Discrete-Event Processes

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network’s universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.     

Constructing p,n-forms from p-forms via the Hodge star operator and the exterior derivative

In this paper, we aim to explore the properties and applications on the operators consisting of the Hodge star operator together with the exterior derivative, whose action on an arbitrary p-form field in n-dimensional spacetimes makes its form degree remain invariant. Such operations are able to generate a variety of p-forms with the even-order derivatives of the p-form. To do this, we first investigate the properties of the operators, such as the Laplace–de Rham operator, the codifferential and their combinations, as well as the applications of the operators in the construction of conserved currents. On the basis of two general p-forms, then we construct a general n-form with higher-order derivatives. Finally, we propose that such an n-form could be applied to define a generalized Lagrangian with respect to a p-form field according to the fact that it includes the ordinary Lagrangians for the p-form and scalar fields as special cases.     

基于模糊PID参数自整定的细胞培养箱温度控制算法

针对细胞培养箱温度控制具有非线性、时滞性、易受干扰且难以建立精确的数学模型的特点,传统的PID控制方法对于快速维持系统箱内温度稳定存在一定的局限性。提出了以温度误差和误差变化率为控制输入,培养箱内温度为控制量的模糊PID参数自整定的温度控制算法,实现了对PID参数的实时在线修正。实验表明,该模糊PID参数自整定温度控制算法,温度从26℃上升到目标温度37℃,建立稳态的时间为2890s,温度超调极小。系统温度控制精度为±0.05℃,并在相同型号的细胞培养箱上同样得到验证。在控制稳定性方面获得了比传统PID控制更好的控温效果,稳定快,极小超调,温度控制精度高,能满足细胞培养箱温度控制的要求。     

Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential V (x) = V₁ e ^2βx + V₂ e ^βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β → -β).     

嵌入原子法研究Ni3Al中点缺陷以及Re择优占位和集团化

基于纯金属元素Ni，Al和Re的基本物理性质，建立了一个Ni-Al-Re三元体系的分析型嵌入原子多体势.结合分子动力学计算了Ni₃Al的平衡晶格常数、弹性模量、结合能、空位形成能以及反位置缺陷形成能，并分析了Ni₃Al中点缺陷的存在形式.计算结果表明，当成分偏离理想化学配比时出现反位置缺陷.同时研究了Re在Ni₃Al中的择优占位以及Re在Ni₃Al和Ni中的集团化行为.计算结果表明，Re在Ni₃Al中优先置换Al的位置，且发现当Re原子团的尺寸接近于11?时，Re原子团的长大趋势变弱.计算结果与实验以及其他的理论计算结果相符合. 关键词： 嵌入原子势 3Al')" href="#">Ni₃Al Re 占位 集团化     

Perturbation,symmetry analysis,Bäcklund and reciprocal transformation for the extended Boussinesq equation in fluid mechanics

In this work, we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics, scientific fields, and ocean engineering. This equation will be reduced to the Korteweg–de Vries equation via using the perturbation analysis. We derive the corresponding vectors, symmetry reduction and explicit solutions for this equation. We readily obtain B?cklund transformation associated with truncated Painlevéexpansion. We also examine the related conservation laws of this equation via using the multiplier method. Moreover, we investigate the reciprocal B?cklund transformations of the derived conservation laws for the first time.     

Rényi Entropy,Signed Probabilities,and the Qubit

The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states.     

Energy conditions of the f(T,B) gravity dark energy model with the validity of thermodynamics

In this article, the analysis of Tsallis holographic dark energy(which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f(T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards f(T,B)=αT~m+βB~n, made possible by the fact that the model is purely accelerating,corresponds to q=-0.54(Mamon and Das 2017 Eur. Phys.J.C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe.With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter,whereas it appears when the model is in the quintessence dominated era.     

Persistence of pierisin-1 activities in the adult cabbage white butterfly,Pieris rapae,during storage after killing

Crude extracts from larvae, pupae and adults of cabbage white butterflies, Pieris rapae and Pieris brassicae, and green-veined butterfly, Pieris napi, have an ability to induce apoptosis in the human cancer cell lines. As apoptosis inducing protein, pierisin-1 and -2 have been isolated from pupae of P. rapae and P. brassicae, respectively, and shown to exhibit DNA ADP-ribosylating activity. Although the highest activity was detected in the late phase of larvae and early phase of pupae, certain activity was found in adult butterflies. In order to investigate distribution of substances having pierisin-like activities in butterflies, many species need to be analyzed. However, fresh samples of larvae and pupae are hard to obtain, especially if samples are of scarce species or from overseas. The usage of adult butterflies is practical to examine the distribution of pierisin-like activity in many species. In this study, we examined the cytotoxicity of crude extracts from adults of P. rapae against HeLa cells and DNA ADP-ribosylation ability during storage for 1, 2 and 8 weeks at room temperature after killing adult butterflies after eclosion. Body weights decreased to 18% for 8 weeks through dehydration. Cytotoxicity of samples from butterfly kept for 1, 2 and 8 weeks decreased to 47, 39 and 22%, respectively, of the control value. DNA ADP-ribosylating activity of the samples also decreased to 30, 27 and 23%. Similar reduction was observed on western blot analysis with anti-pierisin-1 antibody. Fortunately, these results suggest that cytotoxic and DNA ADP-ribosylating activity persists to some extent in the body after killing, at least for 8 weeks. Thus, butterfly adult samples kept for two months at room temperature can still be useful for examination of the presence of substance having pierisin-like activity.