Informational entropy is quantitatively related to similarity and symmetry. Some tacit assumptions regarding their correlation have been shown to be wrong. The Gibbs paradox statement (indistinguishability corresponds to minimum entropy, which is zero) has been rejected. All their correlations are based on the relation that less information content corresponds to more entropy. Higher value of entropy is correlated to higher molecular similarity. The maximum entropy of any system (e.g., a mixture or an assemblage) corresponds to indistinguishability (total loss of information), to perfect symmetry or highest symmetry, and to the highest simplicity. This conforms without exception to all the experimental facts of both dynamic systems and static structures and the related information loss processes. 1.

Leslie Valiant recently proposed a theory of holographic algorithms. These novel algorithms achieve exponential speed-ups for certain computational problems compared to naive algorithms for the same problems. The methodology uses Pfaffians and (planar) perfect matchings as basic computational primitives, and attempts to create exponential cancellations in computation. In this article we survey this new theory of matchgate computations and holographic algorithms.

Introduction Liquid water is the most mysterious substance for natural scientists because of its great importance in the Universe and its versatile abnormal properties are far from being completely understood. It is formed due to hydrogen or, shortly, Hbonds and it is, in fact, its H-bonded pattern with interconnectivity and tortuosity that always plays the role of the key starting point in numerous studies aimed at resolving water paradigm [1] (see also [2]). It has been known for a long time that H-bonded patterns of liquid water and hexagonal ice Ih are tetrahedral [1(a)]. They were also believed to have much more similarities between them. That is why ice was often chosen as a reasonable reference model for the study of an H-bonded water pattern. The aforementioned tetrahedrality originates, in fact, from the tetrahedral charge distribution around c fl E.Kryachko 213 E.Kryachko the oxygen atom in a water monomer possessing t

Symmetry is a measure of indistinguishability. Similarity is a continuous measure of imperfect symmetry. Lewis' remark that "gain of entropy means loss of information" defines the relationship of entropy and information. Three laws of information theory have been proposed. Labeling by introducing nonsymmetry and formatting by introducing symmetry are defined. The function L ( L=lnw, w is the number of microstates, or the sum of entropy and information, L=S+I) of the universe is a constant (the first law of information theory). The entropy S of the universe tends toward a maximum (the second law law of information theory). For a perfect symmetric static structure, the information is zero and the static entropy is the maximum (the third law law of information theory). Based on the Gibbs inequality and the second law of the revised information theory we have proved the similarity principle (a continuous higher similarity-higher entropy relation after the rejection of the Gibbs paradox) and proved the Curie-Rosen symmetry principle (a higher symmetry-higher stability relation) as a special case of the similarity principle. The principles of information minimization and potential energy minimization are compared.

published in

Abstract. As no heat effect and mechanical work are observed, we have a simple experimental resolution of the Gibbs paradox: both the thermodynamic entropy of mixing and the Gibbs free energy change are zero during the formation of any ideal mixtures. Information loss is the driving force of these spontaneous processes. Information is defined as the amount of the compressed data. Information losses due to dynamic motion and static symmetric structure formation are defined as two kinds of entropies – dynamic entropy and static entropy, respectively. There are three laws of information theory, where the first and the second laws are analogs of the two thermodynamic laws. However, the third law of information theory is different: for a solid structure of perfect symmetry (e.g., a perfect crystal), the entropy (static entropy for solid state) S is the maximum. More generally, a similarity principle is set up: if all the other conditions remain constant, the higher the similarity among the components is, the higher the value of entropy of the mixture (for fluid phases) or the assemblage (for a static structure or a system of condensed phases) or any other structure (such as quantum states in quantum mechanics) will be, the more stable the mixture or the assemblage will be, and the more spontaneous the process leading to such a mixture or an assemblage or a chemical bond will be.

Abstract not found

Complex disordered states- from liquids and glasses to exotic quantum matter- are ubiquitous in nature. Their key properties include finite entropy, power-law correlations and emergent organising principles. In spin ice, spin correlations are determined by an ice rules organising principle that stabilises a magnetic state with the same zero point entropy as water ice. The entropy can be manipulated with great precision by a magnetic field: with field parallel to the trigonal axis one obtains quasi two dimensional kagome ice which can be mapped onto a dimer model. Here we use a field tilted slightly away from the trigonal axis to control the dimer statistical weights and realise the unusual critical behaviour predicted by Kasteleyn. Neutron scattering on Ho2Ti2O7 reveals pinch point scattering that characterises the emergent gauge structure of kagome ice; diffuse peaks that shift with field, signaling the Kasteleyn physics; and an unusual critical point.

Ab initio molecular dynamics (AIMD) results on a liquid krypton-water system are presented and compared to recent XAFS results for the radial hydration structure for a Kr atom in liquid water solution. Though these AIMD calculations have important limitations of scale, the comparisons with the liquid solution results are satisfactory and significantly different from the radial distributions extracted from the data on the solid Kr/H2O clathrate hydrate phase. The calculations also produce the coordination number distribution that can be examined for metastable coordination structures suggesting possibilities for clathrate-like organization; none are seen in these results. Clathrate pictures of hydrophobic hydration are discussed, as is the quasichemical theory that should provide a basis for clathrate pictures. Outer shell contributions are discussed and accurately estimated; they are positive and larger than the positive experimental hydration free energy of Kr(aq), implying that inner shell contributions must be negative and of comparable size. Clathrate-like inner shell hydration structures on a Kr atom solute are

This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT-symmetric quantum mechanics are discussed, and some