DOCSLIB.ORG

The Entropic Force in Reissoner-Nordström-De Sitter

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Entropic Force in Reissoner-Nordström-De Sitter Physics Letters B 797 (2019) 134798 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb The entropic force in Reissoner-Nordström-de Sitter spacetime ∗ Li-Chun Zhang a,b, Ren Zhao a,b, a Institute of Theoretical Physics, Shanxi Datong University, Datong 037009, China b Department of Physics, Shanxi Datong University, Datong 037009, China a r t i c l e i n f o a b s t r a c t Article history: We compare the entropic force between the black hole horizon and the cosmological horizon in Received 2 March 2019 Reissoner-Nordström-de Sitter (RN-dS) spacetime with the Lennard-Jones force between two particles. Received in revised form 21 July 2019 It is found that the former has an extraordinary similarity to the latter. We conclude that the black hole Accepted 22 July 2019 horizon and the cosmological horizon are not pure geometric surface, but have a definite “thickness”, Available online 24 July 2019 which is proportional to the radius of the horizons. In the case of no external force, according to different Editor: M. Cveticˇ initial condition, the relative position of the two horizons will experience first accelerated expansion, then decelerated expansion, or first accelerated contraction, then decelerated contraction. Therefore the whole Universe is oscillating. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction nuity is of the first order; and the one with continuous entropy is of the second order. Exactly, for the first-order phase transition The accelerating Universe manifests that it is an asymptotically Gibbs free energy is continuous and its first derivative is not; for de Sitter one. It is a tough issue to study the thermodynamic prop- the second-order phase transition and its first derivative are both erties of black holes in dS space, because the cosmological horizon continuous while the second derivative is discontinuous, such as and the black hole horizon generally have different temperatures. heat capacity, isothermal compressibility and expansion coefficient. The cosmological constant may be a candidate of the dark energy, VdW system, which has no latent heat at the critical point, has the which arouses extensive attention on the thermodynamics of dS second-order phase transition there. Similarly, we found that the space [1–12]. phase transition of RN-dS black hole is of second order, just like Although multiple horizons exist for the black holes in dS space, its RN-AdS counterpart. the thermodynamic quantities of these horizons are all dependent Eight years ago, Verlinde [17]proposed to link gravity with on the black hole mass, electric charge, the cosmological constant. an entropic force. The ensuing conjecture was proved recently From this point of view, the thermodynamic quantities for the [18–20], in a purely classical environment. According to our pre- respective horizons are not independent, but are related to each vious results [15], we calculate the entropic force between the other. On the basis of this consideration, we can introduce effective two horizons, especially the relation between the entropic force thermodynamic quantities, by which we studied the phase transi- and the horizon’s position. Comparing the entropic force with the tion and critical phenomena of four and higher dimensional RN-dS Lennard-Jones force between two particles [21], we find that they black holes. We also derived the entropy of the RN-dS black holes have nearly the same behavior. According to the Lennard-Jones po- by considering the correlations between the black hole horizon and tential, when the distance between the two particles is the diam- the cosmological horizon [13–16]. Treating the cosmological con- eter of the particle, the potential is zero. Similarly, we guess that stant as a variable and relating it to the thermodynamic pressure, the black hole horizon and the cosmological horizon both have a we found that dS black holes have the similar critical behaviors finite thickness. As is well known, a cutoff should be introduced to to that of Van der Waals system. Ehrenfest had ever classified the obtain the black hole entropy [22–24]. However the exact mean- phase transitions: the one corresponding to the entropy disconti- ing of the cutoff is still unknown. As we stated in this paper, if the horizons have a finite thickness, the lower limit of the integral for the black hole entropy cannot take to be at the position of the Corresponding author at: Department of Physics, Shanxi Datong University, Da- * horizon. This can explain the cutoff issue. tong 037009, China. E-mail addresses: [email protected] (L.-C. Zhang), [email protected] The paper is arranged as follows: in Section 2, we first simply (R. Zhao). review the results in Ref. [15] and derive the entropic force be- https://doi.org/10.1016/j.physletb.2019.134798 0370-2693/© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 2 L.-C. Zhang, R. Zhao / Physics Letters B 797 (2019) 134798 tween the two horizons. In Section 3, we compare the entropic force with the Lennard-Jones force between two particles. We de- rive the thickness of the horizons by analogy in Section 4. In the last section, we analyze the oscillation of the two horizon under the entropic force and obtain an oscillating Universe. (We use the units G = h¯ = kB = c = 1.) 2. Entropic force between the two horizons The line element of the RN-dS black hole is given by − ds2 =−h(r)dt2 + h(r) 1dr2 + r2d2, (1) where Fig. 1. f (x) − x curve. 2 2M Q 2 h(r) = 1 − + − r . (2) RNdS black hole is also a thermodynamic system. We can de- r r2 3 rive its entropic force. According to Eq. (3), the entropy from the For RN-dS black hole, the black hole horizon and the cosmo- interaction between the two horizons is logical horizon both depend on the same family of parameters: = 2 M, Q , . All other geometric and thermodynamic quantities can S πrc f (x). (8) be expressed by these parameters. So we think that the two hori- By analogy with Eq. (7), we can define the entropic force of the zons are not independent. There should be some correlations be- RN-dS black hole as tween them. The evolution of the black hole horizon will lead to ∂ S the evolution of the cosmological horizon and vice versa. On the F =−Tef f , (9) ∂r basis of this consideration, we proposed that the total entropy of Tef f the RN-dS black hole should include an correction term describing where Tef f is the effective temperature, and r = rc −r+ = rc(1 − x). the correlations between the two horizons besides their respective In our opinion, the entropic force between the two horizons origi- horizon entropy. Requiring the temperature of the lukewarm black nate from the interactions between them. Thus in the definition of hole equal to the effective temperature, we can derive the correc- the entropic force we are only concerned with the extra correction tion term. The result has been given in [15], which is entropy. In detail, the entropic force is1 ∂ S ∂ Tef f ∂ S ∂ Tef f = 2[ + 2 + ]= + + − Stotal πrc 1 x f (x) Sc, S, (3) ∂rc ∂x ∂x rc ∂rc x rc x F (x) = Tef f ∂ Tef f ∂ Tef f where rc and r+ are the radius of the cosmological horizon and (x − 1) − rc ∂x r ∂rc x the black hole horizon respectively, and we define x = r+/rc , thus c 2[ − 2 + 3 − 5]− 2[ − 3 + 4 − 7] 0 ≤ x ≤ 1. From Eq. (3), the total entropy includes two parts. = x 1 3x 3x x φ 1 3x 3x x = 2 + 2 3 + 4 Sc,+ πrc (1 x ) is the entropy without considering the correla- 4x (1 x ) tion between the two horizons. It is just the sum of the respective + + 4 × 2Af(x) x(1 x )Bf (x) entropy of the two horizons. In fact, the two horizons are not com- , (10) A(x − 1) + x(1 + x4)B = 2 pletely independent. This gives the correction term S πrc f (x), where where = 2[− − 2 + 3 − 4 − 5 + 6 − 7] 8 2(4 − 5x3 − x5) A x 1 3x 6x 5x 4x 9x 6x f (x) = (1 − x3)2/3 − . (4) 5 5(1 − x3) + φ2[3 + 4x4 − 8x7 + 9x8], 2 2 3 5 2 3 4 7 The behavior of f (x) is shown in Fig. 1. B = x [1 − 3x + 3x − x ]−φ [1 − 3x + 3x − x ]. The volume of the system is [25–27] For different values of φ, we depict the F − x curves in the range 0 ≤ x ≤ 1in Fig. 2 (see also Fig. 1). Clearly, the three curves 4π = − = 3 − 3 nearly coincide. The values of horizontal coordinate correspond- V V c V + rc (1 x ). (5) 3 ing to F = 0are x = 0.9748057, x = 0.9748059, and x = 0.9748064 The effective temperature is [15] with the increase of φ. Obviously, the values of φ has almost no effect on the F − x x2[1 − 3x2 + 3x3 − x5]−φ2[1 − 3x3 + 3x4 − x7] curves. In particular, F →+∞ when x → 1. T = , (6) ef f 3 4 4π x rc(1 + x ) 3. Comparison between the entropic force and the = where φ Q /rc is the electric potential at the cosmological hori- Lennard-Jones force zon.
Load more

Recommended publications
  • Inertial Mass of an Elementary Particle from the Holographic Scenario
    Document downloaded from: http://hdl.handle.net/10459.1/62944 The final publication is available at: https://doi.org/10.1142/S0217751X17500439 Copyright (c) World Scientific Publishing, 2017 Inertial mass of an elementary particle from the holographic scenario Jaume Gin´e Departament de Matem`atica, Universitat de Lleida, Catalonia, Spain. E{mail: [email protected] Abstract Various attempts have been made to fully explain the mechanism by which a body has inertial mass. Recently it has been proposed that this mechanism is as follows: when an object accelerates in one direction a dy- namical Rindler event horizon forms in the opposite direction, suppressing Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation in the other side is only slightly reduce by a Hubble-scale Casimir effect. This produces a net Unruh radiation pressure force that always op- poses the acceleration, just like inertia, although the masses predicted are twice those expected, see [17]. In a later work an error was corrected so that its prediction improves to within 26% of the Planck mass, see [10]. In this paper the expression of the inertial mass of a elementary particle is derived from the holographic scenario giving the exact value of the mass of a Planck particle when it is applied to a Planck particle. Keywords: inertial mass; Unruh radiation; holographic scenario, Dark matter, Dark energy, cosmology. PACS 98.80.-k - Cosmology PACS 04.62.+v - Quantum fields in curved spacetime PACS 06.30.Dr - Mass and density 1 Introduction The equivalence principle introduced by Einstein in 1907 assumes the com- plete local physical equivalence of a gravitational field and a corresponding non- inertial (accelerated) frame of reference (Einstein was thinking of his famous elevator experiment).
    [Show full text]
  • Quantization of Black Holes Is One of the Important Issues in Physics [1], and There Has Been No Satisfactory Solution Yet
    Quantization of Black Holes Xiao-Gang He1, 2, 3, 4, ∗ and Bo-Qiang Ma1, 2, 4, † 1School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 2Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617 3Institute of Particle Physics and Cosmology, Department of Physics, Shanghai JiaoTong University, Shanghai 200240 4Center for High-Energy Physics, Peking University, Beijing 100871 Abstract We show that black holes can be quantized in an intuitive and elegant way with results in agreement with conventional knowledge of black holes by using Bohr’s idea of quantizing the motion of an electron inside the atom in quantum mechanics. We find that properties of black holes can be also derived from an Ansatz of quantized entropy ∆S = 4πk∆R/λ, which was suggested in a previous work to unify the black hole entropy formula and Verlinde’s conjecture to explain gravity as an entropic force. Such an Ansatz also explains gravity as an entropic force from quantum effect. This suggests a way to unify gravity with quantum theory. Several interesting and surprising results of black holes are given from which we predict the existence of primordial black holes ranging from Planck scale both in size and energy to big ones in size but with low energy behaviors. PACS numbers: 04.70.Dy, 03.67.-a, 04.70.-s, 04.90.+e arXiv:1003.2510v3 [hep-th] 5 Apr 2010 ∗Electronic address: [email protected] †Electronic address: [email protected] 1 The quantization of black holes is one of the important issues in physics [1], and there has been no satisfactory solution yet.
    [Show full text]
  • Statistical Mechanics of Entropic Forces: Disassembling a Toy
    Home Search Collections Journals About Contact us My IOPscience Statistical mechanics of entropic forces: disassembling a toy This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 Eur. J. Phys. 31 1353 (http://iopscience.iop.org/0143-0807/31/6/005) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 132.239.16.142 The article was downloaded on 06/12/2011 at 21:15 Please note that terms and conditions apply. IOP PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 31 (2010) 1353–1367 doi:10.1088/0143-0807/31/6/005 Statistical mechanics of entropic forces: disassembling a toy Igor M Sokolov Institut fur¨ Physik, Humboldt-Universitat¨ zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany E-mail: [email protected] Received 21 June 2010, in final form 9 August 2010 Published 23 September 2010 Online at stacks.iop.org/EJP/31/1353 Abstract The notion of entropic forces often stays mysterious to students, especially to ones coming from outside physics. Although thermodynamics works perfectly in all cases when the notion of entropic force is used, no effort is typically made to explain the mechanical nature of the forces. In this paper we discuss the nature of entropic forces as conditional means of constraint forces in systems where interactions are taken into account as mechanical constraints and discuss several examples of such forces. We moreover demonstrate how these forces appear within the standard formalism of statistical thermodynamics and within the mechanical approach based on the Pope–Ching equation, making evident their connection with the equipartition of energy.
    [Show full text]
  • Colloidal Matter: Packing, Geometry, and Entropy Vinothan N
    Colloidal matter: packing, geometry, and entropy Vinothan N. Manoharan Harvard John A. Paulson School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge MA 02138 USA This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science volume 349 on August 8, 2015. doi: 10.1126/science.1253751 The many dimensions of colloidal matter. The self-assembly of colloids can be controlled by changing the shape, topology, or patchiness of the particles, by introducing attractions between particles, or by constraining them to a curved surface. All of the assembly phenomena illustrated here can be understood from the interplay between entropy and geometrical constraints. Summary of this review article Background: Colloids consist of solid or liquid particles, each about a few hundred nanometers in size, dispersed in a fluid and kept suspended by thermal fluctuations. While natural colloids are the stuff of paint, milk, and glue, synthetic colloids with well-controlled size distributions and interactions are a model system for understanding phase transitions. These colloids can form crystals and other phases of matter seen in atomic and molecular systems, but because the particles are large enough to be seen under an optical microscope, the microscopic mechanisms of phase transitions can be directly observed. Furthermore, their ability to spontaneously form phases that are ordered on the scale of visible wavelengths makes colloids useful building blocks for optical materials such as photonic crystals. Because the interactions between particles can be altered and the effects on structure directly observed, experiments on colloids offer a controlled approach toward understanding and harnessing self-assembly, a fundamental topic in materials science, condensed matter physics, and biophysics.
    [Show full text]
  • Nov/Dec 2020
    CERNNovember/December 2020 cerncourier.com COURIERReporting on international high-energy physics WLCOMEE CERN Courier – digital edition ADVANCING Welcome to the digital edition of the November/December 2020 issue of CERN Courier. CAVITY Superconducting radio-frequency (SRF) cavities drive accelerators around the world, TECHNOLOGY transferring energy efficiently from high-power radio waves to beams of charged particles. Behind the march to higher SRF-cavity performance is the TESLA Technology Neutrinos for peace Collaboration (p35), which was established in 1990 to advance technology for a linear Feebly interacting particles electron–positron collider. Though the linear collider envisaged by TESLA is yet ALICE’s dark side to be built (p9), its cavity technology is already established at the European X-Ray Free-Electron Laser at DESY (a cavity string for which graces the cover of this edition) and is being applied at similar broad-user-base facilities in the US and China. Accelerator technology developed for fundamental physics also continues to impact the medical arena. Normal-conducting RF technology developed for the proposed Compact Linear Collider at CERN is now being applied to a first-of-a-kind “FLASH-therapy” facility that uses electrons to destroy deep-seated tumours (p7), while proton beams are being used for novel non-invasive treatments of cardiac arrhythmias (p49). Meanwhile, GANIL’s innovative new SPIRAL2 linac will advance a wide range of applications in nuclear physics (p39). Detector technology also continues to offer unpredictable benefits – a powerful example being the potential for detectors developed to search for sterile neutrinos to replace increasingly outmoded traditional approaches to nuclear nonproliferation (p30).
    [Show full text]
  • Book of Abstracts Vol. II
    Symposium A Advanced Materials: From Fundamentals to Applications INVITED LECTURES 1. Potassium hydroxide 2. Potassium hydride 3. Potassium carbonate 4. Sodium hydroxide 5. Sodium hydride 6. Sodium carbonate 7. Calcium hydroxide 8. Calcium carbonate 9. Calcium sulphate 10. Calcium nitrate 11. Calcium chloride 12. Barium hydroxide 13. Barium carbonate 14. Barium sulphate 15. Barium nitrate 16. Barium chloride 17. Aluminium sulphate 18. Aluminium nitrate 19. Aluminium chloride 20. Alum 21. Potassium silicate 22. Potassium silicate 23. Potassium calcium silicate 24. Potassium barium silicate 25. Silicon fluoride 26. Ammonium potassium 27. Ethylene chloride compound Chemical symbols used by Dalton, 19th century ← Previous page: Distilling apparatus from John French’s The art of distillation, London 1651 Symposium A: Advanced Materials A - IL 1 Binuclear Complexes as Tectons in Designing Supramolecular Solid-State Architectures Marius Andruh University of Bucharest, Faculty of Chemistry, Inorganic Chemistry Laboratory Str. Dumbrava Rosie nr. 23, 020464-Bucharest, Romania [email protected] We are currently developing a research project on the use of homo- and heterobinuclear complexes as building-blocks in designing both oligonuclear species and high-dimensionality coordination polymers with interesting magnetic properties. The building-blocks are stable binuclear complexes, where the metal ions are held together by compartmental ligands, or alkoxo- bridged copper(II) complexes. The binuclear nodes are connected through appropriate exo- - 3- III bidentate ligands, or through metal-containing anions (e. g. [Cr(NH3)2(NCS)4] , [M(CN)6] , M = Fe , CrIII). A rich variety of 3d-3d and 3d-4f heterometallic complexes, with interesting architectures and topologies of the spin carriers, has been obtained1.
    [Show full text]
  • Holographic Theory, and Emergent Gravity As an Entropic Force
    Holographic theory, and emergent gravity as an entropic force Liu Tao December 9, 2020 Abstract In this report, we are going to study the holographic principle, and the possibility of describing gravity as an entropic force, independent of the details of the microscopic dynamics. We will first study some of the deep connections between Gravity laws and thermodynamics, which motivate us to consider gravity as an entropic force. Lastly, we will investigate some theoretical criticisms and observational evidences on emergent gravity. 1 Contents 1 Introduction3 2 Black holes thermodynamics and the holographic principle3 2.1 Hawking temperature, entropy..........................3 2.1.1 Uniformly accelerated observer and the Unruh effect.........3 2.1.2 Hawking temperature and black hole entropy..............6 2.2 Holographic principle...............................7 3 Connection between gravity and thermodynamics8 3.1 Motivations (from ideal gas and GR near event horizon)...........8 3.2 Derive Einstein's law of gravity from the entropy formula and thermodynamics 10 3.2.1 the Raychaudhuri equation........................ 10 3.2.2 Einstein's equation from entropy formula and thermodynamics.... 11 4 Gravity as an entropic force 13 4.1 General philosophy................................ 13 4.2 Entropic force in general............................. 13 4.3 Newton's law of gravity as an entropic force.................. 14 4.4 Einstein's law of gravity as an entropic force.................. 15 4.5 New interpretations on inertia, acceleration and the equivalence principle.. 17 5 Theoretical and experimental criticism 18 5.1 Theoretical criticism............................... 18 5.2 Cosmological observations............................ 19 20section.6 2 1 Introduction The holographic principle was inspired by black hole thermodynamics, which conjectures that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected for any extensive quantities.
    [Show full text]
  • UC Riverside UC Riverside Electronic Theses and Dissertations
    UC Riverside UC Riverside Electronic Theses and Dissertations Title A Hybrid Density Functional Theory for Solvation and Solvent-Mediated Interactions Permalink https://escholarship.org/uc/item/4p6713xb Author Jin, Zhehui Publication Date 2012 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA RIVERSIDE A Hybrid Density Functional Theory for Solvation and Solvent-Mediated Interactions A Dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Chemical and Environmental Engineering by Zhehui Jin March 2012 Dissertation Committee: Dr. Jianzhong Wu, Chairperson Dr. Ashok Mulchandani Dr. David Kisailus Copyright by Zhehui Jin 2012 The Dissertation of Zhehui Jin is approved: _________________________________________________ _________________________________________________ _________________________________________________ Committee Chairperson University of California, Riverside Acknowledgements This thesis is the result of five years of work whereby I have been accompanied and supported by many people. I would like to express the most profound appreciation to my advisor, Prof. Jianzhong Wu. He led me to the field of statistical thermodynamics and guided me to define research problems and solve these problems through theoretical approaches. I have been greatly benefited from his wide knowledge and logical way of thinking and gained fruitful achievements during my Ph.D. study. His enthusiasms on research and passion for providing high-quality research works have made a deep impression on me. I am deeply grateful to Dr. Yiping Tang, Prof. Zhengang Wang, Dr. De-en Jiang, Dr. Dong Meng, and Dr. Douglas Henderson who have assisted my research work and led me to different exciting fields of study.
    [Show full text]
  • Liquid Crystalline Phases in Oligonucleotide Solutions
    1TTWOW 0336.6 0SSVNV¥JVZ[P[\P[VKHSS\UPVULKLPZLN\LU[PLSLTLU[P 5LSSLWHNPULJOLZLN\VUVZVUVYPWVY[H[LSL]HYPHU[P KLSSVNVPUKP]PK\H[LWLYHKLN\HYZPJVUZ\JJLZZVHK S 3PTTHNPUL KLSSH 4PULY]H H YHWWYLZLU[HaPVUL 3H KLUVTPUHaPVUL <UP]LYZP[ KLNSP :[\KP KP VNUPLZPNLUaHKP\[PSPaaV0UWHY[PJVSHYL]LUNVUV KLSSH:HWPLUaHJVSSVJH[HZ\SSVZMVUKVKP\UWYVÉSV 4PSHUVYPWVY[H[HPUJHYH[[LYL[PWVNYHÉJV7HSH[PUV WYLZLU[H[LSL]HYPHU[PKPMVYTHYPN\HYKHU[PSHKP KLSSH JP[[ KP 4PSHUV YPJVUVZJPIPSL KH HSJ\UP KLP ;HSLLSLTLU[VJVZ[P[\PZJLWHY[LPU[LNYHU[LKLSSVNV ZWVZPaPVUL KLSSH 4PULY]H YPZWL[[V HSSH ZJYP[[H SL Z\VP LKPÉJP WP² JHYH[[LYPZ[PJP L JPYJVUKH[H KHSSH LUVUW\®WLYULZZ\UTV[P]V]LUPYLTVKPÉJH[V ]HYPHU[PKPJVSVYLLSL]HYPHU[PKPKPTLUZPVULLSH ZJYP[[H<UP]LYZP[HZ:[\KPVY\T4LKPVSHULUZPZ VKVTLZZV IVYH[LWLYV[[PTPaaHYLSHYLZHNYHÉJHKLSSVNVULSSH YPWYVK\aPVULZ\Z\WWVY[PKPKP]LYZVMVYTH[V Doctorate School in Physics, Astrophysics and Applied Physics LIQUID CRYSTALLINE PHASES IN OLIGONUCLEOTIDE SOLUTIONS FIS/03 Doctorate Thesis of: Giuliano ZANCHETTA XX cycle Advisor: Prof. Tommaso BELLINI Co-advisor: Dr. Guido TIANA Director of the school: Prof. Gianpaolo BELLINI Academic year 2006-2007 to Michi, artist of science, and to my women, Betta and Teresa "Le cose tutte quante hanno ordine tra loro, e questo `eforma che l'universo a Dio fa simigliante." (Dante, Paradiso, I, 103) [All things whate'er they be Have order among themselves, and this is form, That makes the universe resemble God] "Il pensiero pi`urisoluto, pi`uostinatamente perseguito, ´eniente in confronto a ci`oche avviene." (Cesare Pavese (1908-1950)) [The most determined, the most stubbornly pursued thought is nothing in comparison with what happens] Abstract In this thesis, we investigate the behavior of short complementary B-form DNA oligomers, 6 to 20 base pairs in length, exhibiting chiral nematic and colum- nar liquid crystal phases, even though such duplexes lack the shape anisotropy required for liquid crystal ordering.
    [Show full text]
  • Protein Folding Proteins
    Protein Folding Proteins: ● Proteins are biopolymers that form most of the cellular machinery ● The function of a protein depends on its 'fold' – its 3D structure Motor Chaperone Walker Levels of Folding: F T P A V L F A H D PRIMARY QUATERNARY K F L A S V T S V TERTIARY SECONDARY The Backbone ● Amino acids linked together R H O by peptide bonds 1 y y C 1 H a N 2 C' N f C' f C a N H 1 2 O R 2 Peptide Bond Steric constraints lead only to a subset of possible angles --> Ramachandran plot Glycine residues can adopt many angles a Helices 3.6 residues/turn b Sheets parallel sheet anti-parallel sheet other topologies possible but much more rare Classes of Folds: ● There are three broad classes of folds: a, b and a+b ● as of today, 103000 known structures --> 1100 folds (SCOP 1.75) alpha class beta class alpha+beta class myoglobin – stores oxygen TIM barrel – 10% of enzymes in muscle tissue streptavadin – used a lot adopt this fold, a great in biotech, binds biotin template for function Databases: SWISSPROT: contains sequence data of proteins – 100,000s of sequences Protein Data Bank (PDB): contains 3D structural data for proteins – 100,000 structures, x-ray & NMR SCOP: classifies all known structures into fold classes ~ 1100 folds Protein Folding: FOLDING amino acid sequence structure DESIGN ● naturally occurring sequences seem to have a unique 3D structure Levinthal paradox: if the polymer doesn't search all of conformation space, how on earth does it find its ground state, and in a reasonable time? if 2 conformation/residue & dt ~ 10-12 ->
    [Show full text]
  • De Sitter Black Holes, Schottky Peaks, and Continuous Heat Engines
    arXiv:1907.05883 de Sitter Black Holes, Schottky Peaks and Continuous Heat Engines Clifford V. Johnson Department of Physics and Astronomy University of Southern California Los Angeles, CA 90089-0484, U.S.A. johnson1 [at] usc [dot] edu Abstract Recent work has uncovered Schottky{like peaks in the temperature dependence of key specific heats of certain black hole thermodynamic systems. They signal a finite window of available energy states for the underlying microscopic degrees of freedom. This paper reports on new families of peaks, found for the Kerr and Reissner–Nordstr¨omblack holes in a spacetime with positive cosmological constant. It is known that a system with a highest energy, when coupled arXiv:1907.05883v3 [hep-th] 2 Aug 2019 to two distinct heat baths, can naturally generate a thermodynamic instability, population inversion, a channel for work output. It is noted that these features are all present for de Sitter black holes. It is shown that there are trajectories in parameter space where they behave as generalized masers, operating as continuous heat engines, doing work by shedding angular momentum. It is suggested that bounds on efficiency due to the second law of thermodynamics for general de Sitter black hole solutions could provide powerful consistency checks. 1 Introduction An examination of the behaviour of certain thermodynamic quantities can provide a wealth of useful information about the underlying microscopic quantum mechanical degrees of freedom, sometimes providing key clues as to the formulation of the underlying model. This has a long history, start- ing with early models of gases provided by Einstein [1] (refined by Debye [2]), that derive the temperature dependence of the specific heat at constant volume, CV (T ) starting from simple sta- tistical mechanical considerations of the basic degrees of freedom (for a review see e.g., refs.
    [Show full text]
  • Durham Research Online
    Durham Research Online Deposited in DRO: 27 September 2016 Version of attached le: Published Version Peer-review status of attached le: Peer-reviewed Citation for published item: Appels, Michael and Gregory, Ruth and Kubiz§n¡ak,David (2016) 'Thermodynamics of accelerating black holes.', Physical review letters., 117 (13). p. 131303. Further information on publisher's website: http://dx.doi.org/10.1103/PhysRevLett.117.131303 Publisher's copyright statement: This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Additional information: Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full DRO policy for further details. Durham University Library, Stockton Road, Durham DH1 3LY, United Kingdom Tel : +44 (0)191 334 3042 | Fax : +44 (0)191 334 2971 https://dro.dur.ac.uk week ending PRL 117, 131303 (2016) PHYSICAL REVIEW LETTERS 23 SEPTEMBER 2016 Thermodynamics of Accelerating Black Holes † ‡ Michael Appels,1,* Ruth Gregory,1,2, and David Kubizňák2, 1Centre for Particle Theory, Durham University, South Road, Durham DH1 3LE, United Kingdom 2Perimeter Institute, 31 Caroline Street, Waterloo, Ontario N2L 2Y5, Canada (Received 6 May 2016; published 21 September 2016) We address a long-standing problem of describing the thermodynamics of an accelerating black hole.
    [Show full text]