Entropy (Order and Disorder)
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Order and Disorder: Poetics of Exception
Order and disorder Página 1 de 19 Daniel Innerarity Order and disorder: Poetics of exception “While working, the mind proceeds from disorder to order. It is important that it maintain resources of disorder until the end, and that the order it has begun to impose on itself does not bind it so completely, does not become such a rigid master, that it cannot change it and make use of its initial liberty” (Paul Valéry 1960, 714). We live at a time when nothing is conquered with absolute security, neither knowledge nor skills. Newness, the ephemeral, the rapid turn-over of information, of products, of behavioral models, the need for frequent adaptations, the demand for flexibility, all give the impression that we live only in the present in a way that hinders stabilization. Imprinting something onto the long term seems less important that valuing the instant and the event. That being said, thought has always been connected to the task of organizing and classifying, with the goal of conferring stability on the disorganized multiplicity of the manifestations of reality. In order to continue making sense, this articulation of the disparate must understand the paradoxes of order and organization. That is what has been going on recently: there has been a greater awareness of disorder and irregularity at the level of concepts and models for action and in everything from science to the theory of organizations. This difficulty is as theoretical as it is practical; it demands that we reconsider disorder in all its manifestations, as disorganization, turbulence, chaos, complexity, or entropy. -
Arxiv:1212.0736V1 [Cond-Mat.Str-El] 4 Dec 2012 Non-Degenerate Polarized Phase
Disorder by disorder and flat bands in the kagome transverse field Ising model M. Powalski,1 K. Coester,1 R. Moessner,2 and K. P. Schmidt1, ∗ 1Lehrstuhl f¨urTheoretische Physik 1, TU Dortmund, Germany 2Max Planck Institut f¨urkomplexe Systeme, D-01187 Dresden, Germany (Dated: August 10, 2018) We study the transverse field Ising model on a kagome and a triangular lattice using high-order series expansions about the high-field limit. For the triangular lattice our results confirm a second- order quantum phase transition in the 3d XY universality class. Our findings for the kagome lattice indicate a notable instance of a disorder by disorder scenario in two dimensions. The latter follows from a combined analysis of the elementary gap in the high- and low-field limit which is shown to stay finite for all fields h. Furthermore, the lowest one-particle dispersion for the kagome lattice is extremely flat acquiring a dispersion only from order eight in the 1=h limit. This behaviour can be traced back to the existence of local modes and their breakdown which is understood intuitively via the linked cluster expansion. PACS numbers: 75.10.Jm, 05.30.Rt, 05.50.+q,75.10.-b I. INTRODUCTION for arbitrary transverse fields providing a novel instance of disorder by disorder in which quantum fluctuations The interplay of geometric frustration and quantum select a quantum disordered state out of the classically fluctuations in magnetic systems provides a fascinating disordered ground-state manifold. There is no conclu- field of research. It gives rise to a multitude of quan- sive evidence excluding a possible ordering of the kagome tum phases manifesting novel phenomena of quantum transverse field Ising model (TFIM) and its global phase order and disorder, featuring prominent examples such diagram remains unsettled. -
Bluff Your Way in the Second Law of Thermodynamics
Bluff your way in the Second Law of Thermodynamics Jos Uffink Department of History and Foundations of Science Utrecht University, P.O.Box 80.000, 3508 TA Utrecht, The Netherlands e-mail: uffi[email protected] 5th July 2001 ABSTRACT The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-(a)symmetry and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Caratheodory´ and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-asymmetry plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. KEY WORDS: Thermodynamics, Second Law, Irreversibility, Time-asymmetry, Arrow of Time. 1 INTRODUCTION There is a famous lecture by the British physicist/novelist C. P. Snow about the cul- tural abyss between two types of intellectuals: those who have been educated in literary arts and those in the exact sciences. This lecture, the Two Cultures (1959), characterises the lack of mutual respect between them in a passage: A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have 1 with considerable gusto been expressing their incredulity at the illiteracy of sci- entists. -
Order and Disorder in Liquid-Crystalline Elastomers
Adv Polym Sci (2012) 250: 187–234 DOI: 10.1007/12_2010_105 # Springer-Verlag Berlin Heidelberg 2011 Published online: 3 December 2010 Order and Disorder in Liquid-Crystalline Elastomers Wim H. de Jeu and Boris I. Ostrovskii Abstract Order and frustration play an important role in liquid-crystalline polymer networks (elastomers). The first part of this review is concerned with elastomers in the nematic state and starts with a discussion of nematic polymers, the properties of which are strongly determined by the anisotropy of the polymer backbone. Neutron scattering and X-ray measurements provide the basis for a description of their conformation and chain anisotropy. In nematic elastomers, the macroscopic shape is determined by the anisotropy of the polymer backbone in combination with the elastic response of elastomer network. The second part of the review concentrates on smectic liquid-crystalline systems that show quasi-long-range order of the smectic layers (positional correlations that decay algebraically). In smectic elasto- mers, the smectic layers cannot move easily across the crosslinking points where the polymer backbone is attached. Consequently, layer displacement fluctuations are suppressed, which effectively stabilizes the one-dimensional periodic layer structure and under certain circumstances can reinstate true long-range order. On the other hand, the crosslinks provide a random network of defects that could destroy the smectic order. Thus, in smectic elastomers there exist two opposing tendencies: the suppression of layer displacement fluctuations that enhances trans- lational order, and the effect of random disorder that leads to a highly frustrated equilibrium state. These effects can be investigated with high-resolution X-ray diffraction and are discussed in some detail for smectic elastomers of different topology. -
Calculating the Configurational Entropy of a Landscape Mosaic
Landscape Ecol (2016) 31:481–489 DOI 10.1007/s10980-015-0305-2 PERSPECTIVE Calculating the configurational entropy of a landscape mosaic Samuel A. Cushman Received: 15 August 2014 / Accepted: 29 October 2015 / Published online: 7 November 2015 Ó Springer Science+Business Media Dordrecht (outside the USA) 2015 Abstract of classes and proportionality can be arranged (mi- Background Applications of entropy and the second crostates) that produce the observed amount of total law of thermodynamics in landscape ecology are rare edge (macrostate). and poorly developed. This is a fundamental limitation given the centrally important role the second law plays Keywords Entropy Á Landscape Á Configuration Á in all physical and biological processes. A critical first Composition Á Thermodynamics step to exploring the utility of thermodynamics in landscape ecology is to define the configurational entropy of a landscape mosaic. In this paper I attempt to link landscape ecology to the second law of Introduction thermodynamics and the entropy concept by showing how the configurational entropy of a landscape mosaic Entropy and the second law of thermodynamics are may be calculated. central organizing principles of nature, but are poorly Result I begin by drawing parallels between the developed and integrated in the landscape ecology configuration of a categorical landscape mosaic and literature (but see Li 2000, 2002; Vranken et al. 2014). the mixing of ideal gases. I propose that the idea of the Descriptions of landscape patterns, processes of thermodynamic microstate can be expressed as unique landscape change, and propagation of pattern-process configurations of a landscape mosaic, and posit that relationships across scale and through time are all the landscape metric Total Edge length is an effective governed and constrained by the second law of measure of configuration for purposes of calculating thermodynamics (Cushman 2015). -
Order and Disorder in Nature- G
DEVELOPMENT OF PHYSICS-Order And Disorder In Nature- G. Takeda ORDER AND DISORDER IN NATURE G. Takeda The University of Tokyo and Tohoku University, Sendai, Japan Keywords:order,disorder,entropy,fluctuation,phasetransition,latent heat, phase diagram, critical point, free energy, spontaneous symmetry breaking, open system, convection current, Bernard cell, crystalline solid, lattice structure, lattice vibration, phonon, magnetization, Curie point, ferro-paramagnetic transition, magnon, correlation function, correlation length, order parameter, critical exponent, renormalization group method, non-equilibrium process, Navier-Stokes equation, Reynold number, Rayleigh number, Prandtl number, turbulent flow, Lorentz model, laser. Contents 1. Introduction 2. Structure of Solids and Liquids 2.1.Crystalline Structure of Solids 2.2.Liquids 3. Phase Transitions and Spontaneous Broken Symmetry 3.1.Spontaneous Symmetry Breaking 3.2.Order Parameter 4. Non-equilibrium Processes Acknowledgements Glossary Bibliography Biographical Skectch Summary Order-disorder problems are a rapidly developing subject not only in physics but also in all branches of science. Entropy is related to the degree of order in the structure of a system, and the second law of thermodynamics states that the system should change from a more ordered state to a less ordered one as long as the system is isolated from its surroundings.UNESCO – EOLSS Phase transitions of matter are the most well studied order-disorder transitions and occur at certain fixed values of dynamical variables such as temperature and pressure. In general, the degreeSAMPLE of order of the atomic orCHAPTERS molecular arrangement in matter will change by a phase transition and the phase at lower temperature than the transition temperature is more ordered than that at higher temperature. -
The Theory of Dissociation”
76 Bull. Hist. Chem., VOLUME 34, Number 2 (2009) PRIMARY DOCUMENTS “The Theory of Dissociation” A. Horstmann Annalen der Chemie und Pharmacie, 1873, 170, 192-210. W. Thomson was the first to take note of one of (Received 11 October 1873) the consequences of the mechanical theory of heat (1) - namely that the entire world is continuously approaching, It is characteristic of dissociation phenomena that a via the totality of all natural processes, a limiting state in reaction, in which heat overcomes the force of chemical which further change is impossible. Repose and death attraction, occurs for only a portion of a substance, even will then reign over all and the end of the world will though all of its parts have been equally exposed to the have arrived. same influences. In the remaining portion, the forces of chemical attraction, which are the only reason for the Clausius (2) knew how to give this conclusion a reaction to proceed in the opposite direction, maintain mathematical form by constructing a quantity—the the upper hand. Hence, for such reactions there is a entropy—which increases during all natural changes limiting state which the molecular system in question but which cannot be decreased by any known force of approaches irrespective of the initial state and, once it is nature. The limiting state is, therefore, reached when reached, neither heat nor chemical forces can produce the entropy of the world is as large as possible. Then further change so long as the external conditions remain the only possible processes that can occur are those for constant. -
Equilibrium Phases of Dipolar Lattice Bosons in the Presence of Random Diagonal Disorder
Equilibrium phases of dipolar lattice bosons in the presence of random diagonal disorder C. Zhang,1 A. Safavi-Naini,2 and B. Capogrosso-Sansone3 1Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma ,73019, USA 2JILA , NIST and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA 3Department of Physics, Clark University, Worcester, Massachusetts, 01610, USA Ultracold gases offer an unprecedented opportunity to engineer disorder and interactions in a controlled manner. In an effort to understand the interplay between disorder, dipolar interaction and quantum degeneracy, we study two-dimensional hard-core dipolar lattice bosons in the presence of on-site bound disorder. Our results are based on large-scale path-integral quantum Monte Carlo simulations by the Worm algorithm. We study the ground state phase diagram at fixed half-integer filling factor for which the clean system is either a superfluid at lower dipolar interaction strength or a checkerboard solid at larger dipolar interaction strength. We find that, even for weak dipolar interaction, superfluidity is destroyed in favor of a Bose glass at relatively low disorder strength. Interestingly, in the presence of disorder, superfluidity persists for values of dipolar interaction strength for which the clean system is a checkerboard solid. At fixed disorder strength, as the dipolar interaction is increased, superfluidity is destroyed in favor of a Bose glass. As the interaction is further increased, the system eventually develops extended checkerboard patterns in the density distribution. Due to the presence of disorder, though, grain boundaries and defects, responsible for a finite residual compressibility, are present in the density distribution. -
REVIEW Theory of Displacive Phase Transitions in Minerals
American Mineralogist, Volume 82, pages 213±244, 1997 REVIEW Theory of displacive phase transitions in minerals MARTIN T. DOVE Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K. ABSTRACT A lattice-dynamical treatment of displacive phase transitions leads naturally to the soft- mode model, in which the phase-transition mechanism involves a phonon frequency that falls to zero at the transition temperature. The basic ideas of this approach are reviewed in relation to displacive phase transitions in silicates. A simple free-energy model is used to demonstrate that Landau theory gives a good approximation to the free energy of the transition, provided that the entropy is primarily produced by the phonons rather than any con®gurational disorder. The ``rigid unit mode'' model provides a physical link between the theory and the chemical bonds in silicates and this allows us to understand the origin of the transition temperature and also validates the application of the soft-mode model. The model is also used to reappraise the nature of the structures of high-temperature phases. Several issues that remain open, such as the origin of ®rst-order phase transitions and the thermodynamics of pressure-induced phase transitions, are discussed. INTRODUCTION represented in Figure 1. In each case, the phase transitions involve small translations and rotations of the (Si,Al)O The study of phase transitions extends back a century 4 tetrahedra. One of the most popular of the new devel- to the early work on quartz, ferromagnets, and liquid-gas opments in the theory of displacive phase transitions in phase equilibrium. -
Entropy: Is It What We Think It Is and How Should We Teach It?
Entropy: is it what we think it is and how should we teach it? David Sands Dept. Physics and Mathematics University of Hull UK Institute of Physics, December 2012 We owe our current view of entropy to Gibbs: “For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the system that do not alter its energy, the variation of its entropy shall vanish or be negative.” Equilibrium of Heterogeneous Substances, 1875 And Maxwell: “We must regard the entropy of a body, like its volume, pressure, and temperature, as a distinct physical property of the body depending on its actual state.” Theory of Heat, 1891 Clausius: Was interested in what he called “internal work” – work done in overcoming inter-particle forces; Sought to extend the theory of cyclic processes to cover non-cyclic changes; Actively looked for an equivalent equation to the central result for cyclic processes; dQ 0 T Clausius: In modern thermodynamics the sign is negative, because heat must be extracted from the system to restore the original state if the cycle is irreversible . The positive sign arises because of Clausius’ view of heat; not caloric but still a property of a body The transformation of heat into work was something that occurred within a body – led to the notion of “equivalence value”, Q/T Clausius: Invented the concept “disgregation”, Z, to extend the ideas to irreversible, non-cyclic processes; TdZ dI dW Inserted disgregation into the First Law; dQ dH TdZ 0 Clausius: Changed the sign of dQ;(originally dQ=dH+AdL; dL=dI+dW) dHdQ Derived; dZ 0 T dH Called; dZ the entropy of a body. -
Biochemical Thermodynamics
© Jones & Bartlett Learning, LLC. NOT FOR SALE OR DISTRIBUTION CHAPTER 1 Biochemical Thermodynamics Learning Objectives 1. Defi ne and use correctly the terms system, closed, open, surroundings, state, energy, temperature, thermal energy, irreversible process, entropy, free energy, electromotive force (emf), Faraday constant, equilibrium constant, acid dissociation constant, standard state, and biochemical standard state. 2. State and appropriately use equations relating the free energy change of reactions, the standard-state free energy change, the equilibrium constant, and the concentrations of reactants and products. 3. Explain qualitatively and quantitatively how unfavorable reactions may occur at the expense of a favorable reaction. 4. Apply the concept of coupled reactions and the thermodynamic additivity of free energy changes to calculate overall free energy changes and shifts in the concentrations of reactants and products. 5. Construct balanced reduction–oxidation reactions, using half-reactions, and calculate the resulting changes in free energy and emf. 6. Explain differences between the standard-state convention used by chemists and that used by biochemists, and give reasons for the differences. 7. Recognize and apply correctly common biochemical conventions in writing biochemical reactions. Basic Quantities and Concepts Thermodynamics is a system of thinking about interconnections of heat, work, and matter in natural processes like heating and cooling materials, mixing and separation of materials, and— of particular interest here—chemical reactions. Thermodynamic concepts are freely used throughout biochemistry to explain or rationalize chains of chemical transformations, as well as their connections to physical and biological processes such as locomotion or reproduction, the generation of fever, the effects of starvation or malnutrition, and more. -
V320140108.Pdf
1Department of Applied Science and Technology, Politecnico di Torino, Italy Abstract In this paper we are translating and discussing one of the scientific treatises written by Robert Grosseteste, the De Calore Solis, On the Heat of the Sun. In this treatise, the medieval philosopher analyses the nature of heat. Keywords: History of Science, Medieval Science 1. Introduction some features: he tells that Air is wet and hot, Fire is Robert Grosseteste (c. 1175 – 1253), philosopher and hot and dry, Earth is dry and cold, and the Water is bishop of Lincoln from 1235 AD until his death, cold and wet [5]. And, because the above-mentioned wrote several scientific papers [1]; among them, quite four elements are corruptible, Aristotle added the remarkable are those on optics and sound [2-4]. In incorruptible Aether as the fifth element, or essence, [5], we have recently proposed a translation and the quintessence, and since we do not see any discussion of his treatise entitled De Impressionibus changes in the heavenly regions, the stars and skies Elementorum, written shortly after 1220; there, above the Moon must be made of it. Grosseteste is talking about some phenomena involving the four classical elements (air, water, fire The Hellenistic period, a period between the death of and earth), in the framework of an Aristotelian Alexander the Great in 323 BC and the emergence of physics of the atmosphere. This treatise on elements ancient Rome, saw the flourishing of science. In shows the role of heat in phase transitions and in the Egypt of this Hellenistic tradition, under the atmospheric phenomena.