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Entropy

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Full-Text Articles in Physics

Language, Coded Instructions And The Interaction With Thermodynamics, Andy C. Mcintosh Dec 2023

Language, Coded Instructions And The Interaction With Thermodynamics, Andy C. Mcintosh

Proceedings of the International Conference on Creationism

The theme of the 9th ICC is Developing and Systematizing the Creation Model of Origins. Following this theme, the proposed paper seeks to establish a rigorous and systematic approach to the important area of information and its interface with the substrate on which the information is expressed. This must first involve the understanding of the laws of thermodynamics not only for isolated systems but for closed (where only energy is allowed to cross the boundary) and open systems (where both matter and energy are allowed to cross the boundary). This is particularly an issue with the second law of …


Direct Calculation Of Configurational Entropy: Pair Correlation Functions And Disorder, Clifton C. Sluss Aug 2022

Direct Calculation Of Configurational Entropy: Pair Correlation Functions And Disorder, Clifton C. Sluss

Doctoral Dissertations

Techniques such as classical molecular dynamics [MD] simulation provide ready access to the thermodynamic data of model material systems. However, the calculation of the Helmholtz and Gibbs free energies remains a difficult task due to the tedious nature of extracting accurate values of the excess entropy from MD simulation data. Thermodynamic integration, a common technique for the calculation of entropy requires numerous simulations across a range of temperatures. Alternative approaches to the direct calculation of entropy based on functionals of pair correlation functions [PCF] have been developed over the years. This work builds upon the functional approach tradition by extending …


A Super Fast Algorithm For Estimating Sample Entropy, Weifeng Liu, Ying Jiang, Yuesheng Xu Apr 2022

A Super Fast Algorithm For Estimating Sample Entropy, Weifeng Liu, Ying Jiang, Yuesheng Xu

Mathematics & Statistics Faculty Publications

: Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as − log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m + 1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N2) or …


Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat Jan 2022

Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat

Publications and Research

We previously proposed that entanglement across a planar surface can be obtained from the partition function on a Euclidean hourglass geometry. Here we extend the prescription to spherical entangling surfaces in conformal field theory. We use the prescription to evaluate log terms in the entropy of a conformal field theory in two dimensions, a conformally coupled scalar in four dimensions, and a Maxwell field in four dimensions. For Maxwell we reproduce the extractable entropy obtained by Soni and Trivedi. We take this as evidence that the hourglass prescription provides a Euclidean technique for evaluating extractable entropy in quantum field theory.


The Measure Aspect Of Quantum Uncertainty, Of Entanglement, And The Associated Entropies, Ivan Horváth Sep 2021

The Measure Aspect Of Quantum Uncertainty, Of Entanglement, And The Associated Entropies, Ivan Horváth

Physics and Astronomy Faculty Publications

Indeterminacy associated with the probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here, we express it as an effective amount (measure) of distinct outcomes instead. The resulting μ-uncertainties are described by the effective number theory whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive μ-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the μ-entropies, convey how many degrees of freedom are effectively involved in a given …


The Foundations Of Inference And Its Application To Fundamental Physics, Nicholas Matthew Carrara Aug 2021

The Foundations Of Inference And Its Application To Fundamental Physics, Nicholas Matthew Carrara

Legacy Theses & Dissertations (2009 - 2024)

This thesis concerns the foundations of inference – probability theory,entropic inference, information geometry, etc. – and its application to the Entropic Dynamics (ED) approach to Quantum Mechanics (QM) [21, 22, 41, 53, 56–61, 150–153, 165, 195, 196, 268]. The first half of this thesis, chapters 2-6, concern the development of the inference framework. We begin in chapter 2 by discussing de- ductive inference, which involves formal logic and it’s role in access- ing the truth of propositions. We eventually discover that deductive inference is incomplete, in that it can’t address situations in which we have incomplete information. This necessitates a …


Quantitative And Qualitative Comparison Study Between Classification Methods On Normal And Abnormal (With A Coronavirus ) Lung Images, Hala Kadhim Hasan, Ayad A. Al-Ani, Noor Z. Al-Khazraji Jul 2021

Quantitative And Qualitative Comparison Study Between Classification Methods On Normal And Abnormal (With A Coronavirus ) Lung Images, Hala Kadhim Hasan, Ayad A. Al-Ani, Noor Z. Al-Khazraji

Al-Qadisiyah Journal of Pure Science

Classification is concerned with establishing criteria that can be used to identify or distinguish different populations of objects that appear in images. In this paper Supervised and unsupervised classification method applied on normal, abnormal (with a coronavirus) ct- lung images (which it took from Al shaikh zaeid Hospital) to study the quantitative and qualitative properties of these two categories. The analysis of performance with default quantitative parameters revealed that (kurtosis, skewness, entropy, Stander deviation (STD), mean). We found that: Qualitative (as seen) of abnormal lung images after applying Supervisors classification are better than the qualitative of abnormal lung images after …


The Entropic Dynamics Of Relativistic Quantum Fields In Curved Space-Time, Selman Ipek Jan 2021

The Entropic Dynamics Of Relativistic Quantum Fields In Curved Space-Time, Selman Ipek

Legacy Theses & Dissertations (2009 - 2024)

It has often been the case in history that the laws of physics have been used as the framework for understanding and implementing information processing. The tacit assumption is that the laws of physics are fundamental and that the notion of information is derived from these laws. Here we take the opposite view: the laws of physics are an application of the rules for processing information. The inferential framework of entropic dynamics (ED) has previously been developed by A. Caticha for the purposes of understanding and deriving quantum theory, in much the same way that E.T. Jaynes used the MaxEnt …


Protein Conformational Entropy Is Not Slaved To Water, Bryan S Marques, Matthew A Stetz, Christine Jorge, Kathleen G Valentine, A Joshua Wand, Nathaniel V Nucci Oct 2020

Protein Conformational Entropy Is Not Slaved To Water, Bryan S Marques, Matthew A Stetz, Christine Jorge, Kathleen G Valentine, A Joshua Wand, Nathaniel V Nucci

Faculty Scholarship for the College of Science & Mathematics

Conformational entropy can be an important element of the thermodynamics of protein functions such as the binding of ligands. The observed role for conformational entropy in modulating molecular recognition by proteins is in opposition to an often-invoked theory for the interaction of protein molecules with solvent water. The "solvent slaving" model predicts that protein motion is strongly coupled to various aspects of water such as bulk solvent viscosity and local hydration shell dynamics. Changes in conformational entropy are manifested in alterations of fast internal side chain motion that is detectable by NMR relaxation. We show here that the fast-internal side …


The Crisis Of Communication In The Information Age: Revisiting C.P. Snow's Two Cultures In The Era Of Fake News, Aaron Green Jul 2020

The Crisis Of Communication In The Information Age: Revisiting C.P. Snow's Two Cultures In The Era Of Fake News, Aaron Green

Irish Communication Review

The purpose of this paper is to revisit C.P. Snow’s “Two Cultures” lecture in light of the cultural dominance of information technology. The crisis of communication in the information age, whether in fake news, political polarisation or science denial, has come about because both scientific and literary cultures, in seeking a world without entropy, have inadvertently stumbled upon a world without meaning. In order to explain how this has happened, the paper first explores Snow's challenge: to describe the second law of thermodynamics. The paper then provides a description of entropy that is neutral with regard to thermodynamics and information, …


Measuring And Modeling Information Flow On Social Networks, Tyson Charles Pond Jan 2020

Measuring And Modeling Information Flow On Social Networks, Tyson Charles Pond

Graduate College Dissertations and Theses

With the rise of social media, researchers have become increasingly interested in understanding how individuals inform, influence, and interact with others in their social network and how the network mediates the flow of information. Previous research on information flow has primarily used models of contagion to study the adoption of a technology, propagation of purchase recommendations, or virality of online activity. Social (or "complex") contagions spread differently than biological ("simple") contagions. A limitation when researchers validate contagion models is that they neglect much of the massive amounts of data now available through online social networks. Here we model a recently …


Impact Of Anharmonicity On The Vibrational Entropy And Specific Heat Of Uo₂, M. S. Bryan, J. W. L. Pang, B. C. Larson, Aleksandr V. Chernatynskiy, D. L. Abernathy, K. Gofryk, M. E. Manley, For Full List Of Authors, See Publisher's Website. Jun 2019

Impact Of Anharmonicity On The Vibrational Entropy And Specific Heat Of Uo₂, M. S. Bryan, J. W. L. Pang, B. C. Larson, Aleksandr V. Chernatynskiy, D. L. Abernathy, K. Gofryk, M. E. Manley, For Full List Of Authors, See Publisher's Website.

Physics Faculty Research & Creative Works

The impact of anharmonicity on the vibrational entropy and heat capacity of UO2 has been investigated from 10 to 1200 K using inelastic neutron-scattering measurements of the phonon density of states (PDOS). Small changes in the PDOS are observed from 10 to 295 K, with more noticeable changes appearing in the 750- and 1200-K data. The specific heat determined from the PDOS measurements is in agreement with macroscopic specific heat measurements, and the overall impact of nondilation anharmonicity on the specific heat has been shown to be less than 2%. An analysis of the phonon measurements shows that the softening …


Novel Maximum Entrophy Method For The Average Survival Time Differences Between Two Groups, Joscelyne Guzman - Gonzalez Jan 2019

Novel Maximum Entrophy Method For The Average Survival Time Differences Between Two Groups, Joscelyne Guzman - Gonzalez

Open Access Theses & Dissertations

We suggest a Maximum Likelihood estimator for the Average Survival Time Difference between two groups, based on the extra time in which should be added to one group to produce the maximum entropy of the result. The estimator is calculated only from time to event data, does not assume hazard proportionality and provides directly the magnitude of the clinical differences between the groups. Our Monte Carlo simulations show that, even at low sample numbers the estimator is a reliable predictor for the clinical differences between the groups, and therefore can be used to estimate from preliminary data whether or not …


Radical Social Ecology As Deep Pragmatism: A Call To The Abolition Of Systemic Dissonance And The Minimization Of Entropic Chaos, Arielle Brender May 2018

Radical Social Ecology As Deep Pragmatism: A Call To The Abolition Of Systemic Dissonance And The Minimization Of Entropic Chaos, Arielle Brender

Student Theses 2015-Present

This paper aims to shed light on the dissonance caused by the superimposition of Dominant Human Systems on Natural Systems. I highlight the synthetic nature of Dominant Human Systems as egoic and linguistic phenomenon manufactured by a mere portion of the human population, which renders them inherently oppressive unto peoples and landscapes whose wisdom were barred from the design process. In pursuing a radical pragmatic approach to mending the simultaneous oppression and destruction of the human being and the earth, I highlight the necessity of minimizing entropic chaos caused by excess energy expenditure, an essential feature of systems that aim …


Magnetic And Magnetocaloric Properties Of Co2-Xfexvga Heusler Alloys, K. Schroeder, J. Waybright, P. Kharel, W. Zhang, S. Valloppilly, J. Herran, P. Lukashev, Y. Huh, R. Skomsk, D. J. Sellmyer May 2018

Magnetic And Magnetocaloric Properties Of Co2-Xfexvga Heusler Alloys, K. Schroeder, J. Waybright, P. Kharel, W. Zhang, S. Valloppilly, J. Herran, P. Lukashev, Y. Huh, R. Skomsk, D. J. Sellmyer

Faculty Publications

The magnetic and magnetocaloric properties of iron-substituted Co2VGa alloys, Co2-xFexVGa (x = 0, 0.1, 0.15, 0.2, 0.3), were investigated. The Fe-substituted samples, prepared by arc melting, melt spinning, and annealing, crystallized in the L2(1) Heusler structure, without any secondary phases. The Curie temperature and high-field magnetization at 50 K decreased from 345 K and 44 emu/g (1.90 mu(B)/f.u.) for Co2VGa to 275 K and 39 emu/g (1.66 mu(B)/f.u.) for Co1.7Fe0.3VGa, respectively, but the maximum entropy change remained almost insensitive to Fe concentration for x 1.85Fe0.15VGa. First-principle …


Nature Of Entropy In A Scalar-Tensor Theory Of Gravity, Onur Siğinç, Mustafa Salti, Hi̇lmi̇ Yanar, Oktay Aydoğdu Jan 2018

Nature Of Entropy In A Scalar-Tensor Theory Of Gravity, Onur Siğinç, Mustafa Salti, Hi̇lmi̇ Yanar, Oktay Aydoğdu

Turkish Journal of Physics

This work is devoted to studying the generalized nature of the entropy function in a specific form of the scalar-tensor-vector (STeVe) theory of gravity for the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in the state of thermal equilibrium. For this purpose, we define an equilibrium picture of thermodynamics by making use of a suitable set of the dark energy density and dark pressure descriptions, which defines an energy-momentum tensor obeying the local energy conservation law. Furthermore, we also discuss our results numerically in order to get additional implications.


The Entropic Dynamics Approach To The Paradigmatic Quantum Mechanical Phenomena, Susan Difranzo Jan 2018

The Entropic Dynamics Approach To The Paradigmatic Quantum Mechanical Phenomena, Susan Difranzo

Legacy Theses & Dissertations (2009 - 2024)

Standard Quantum Mechanics, although successful in terms of calculating and predicting


The Inferential Design Of Entropy And Its Application To Quantum Measurements, Kevin Vanslette Jan 2018

The Inferential Design Of Entropy And Its Application To Quantum Measurements, Kevin Vanslette

Legacy Theses & Dissertations (2009 - 2024)

This thesis synthesizes probability and entropic inference with Quantum Mechanics and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools \emph{designed} for the purpose of updating probability distributions and density matrices, respectively [1]. The derivation of the standard and quantum relative entropy are completed in tandem following the same inferential principles and design criteria. This provides the first design derivation of the quantum relative entropy while also reducing the number of required design criteria to two.


Neuronal Correlation Parameter In The Idea Of Thermodynamic Entropy Of An N-Body Gravitationally Bounded System, Ioannis Haranas, Ioannis Gkigkitzis, Ilias S. Kotsireas, Carlos Austerlitz Sep 2017

Neuronal Correlation Parameter In The Idea Of Thermodynamic Entropy Of An N-Body Gravitationally Bounded System, Ioannis Haranas, Ioannis Gkigkitzis, Ilias S. Kotsireas, Carlos Austerlitz

Physics and Computer Science Faculty Publications

Understanding how the brain encodes information and performs computation requires statistical and functional analysis. Given the complexity of the human brain, simple methods that facilitate the interpretation of statistical correlations among different brain regions can be very useful. In this report we introduce a numerical correlation measure that may serve the interpretation of correlational neuronal data, and may assist in the evaluation of different brain states. The description of the dynamical brain system, through a global numerical measure may indicate the presence of an action principle which may facilitate a application of physics principles in the study of the human …


Some 2-Categorical Aspects In Physics, Arthur Parzygnat Sep 2016

Some 2-Categorical Aspects In Physics, Arthur Parzygnat

Dissertations, Theses, and Capstone Projects

2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description …


Possible Signatures Of Dissipation From Time-Series Analysis Techniques Using A Turbulent Laboratory Magnetohydrodynamic Plasma, D. A. Schaffner, Michael R. Brown, Ariel B. Rock , '16 May 2016

Possible Signatures Of Dissipation From Time-Series Analysis Techniques Using A Turbulent Laboratory Magnetohydrodynamic Plasma, D. A. Schaffner, Michael R. Brown, Ariel B. Rock , '16

Physics & Astronomy Faculty Works

The frequency spectrum of magnetic fluctuations as measured on the Swarthmore Spheromak Experiment is broadband and exhibits a nearly Kolmogorov 5/3 scaling. It features a steepening region which is indicative of dissipation of magnetic fluctuation energy similar to that observed in fluid and magnetohydrodynamic turbulence systems. Two non-spectrum based time-series analysis techniques are implemented on this data set in order to seek other possible signatures of turbulent dissipation beyond just the steepening of fluctuation spectra. Presented here are results for the flatness, permutation entropy, and statistical complexity, each of which exhibits a particular character at spectral steepening scales which can …


The Role Of Matp, Zapa And Zapb In Chromosomal Organization And Dynamics In Escherichia Coli, Jaana Männik, Daniel E. Castillo, Da Yang, George Siopsis, Jaan Männik Jan 2016

The Role Of Matp, Zapa And Zapb In Chromosomal Organization And Dynamics In Escherichia Coli, Jaana Männik, Daniel E. Castillo, Da Yang, George Siopsis, Jaan Männik

Physics and Astronomy Publications and Other Works

Despite extensive research over several decades, a comprehensive view of how the Escherichia coli chromosome is organized within the nucleoid, and how two daughter chromosomes segregate has yet to emerge. Here we investigate the role of the MatP, ZapA and ZapB proteins in organizing the replication terminus (Ter) region and in the chromosomal segregation process. Quantitative image analysis of the fluorescently labeled Ter region shows that the replication terminus attaches to the divisome in a single segment along the perimeter of the cell in a MatP, ZapA and ZapB-dependent manner. The attachment does not significantly affect the bulk chromosome segregation …


Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes Oct 2015

Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the …


Identifying Student Difficulties With Heat Engines, Entropy, And The Carnot Cycle, Trevor I. Smith, Warren M. Christensen, Donald B. Mountcastle, John R. Thompson Sep 2015

Identifying Student Difficulties With Heat Engines, Entropy, And The Carnot Cycle, Trevor I. Smith, Warren M. Christensen, Donald B. Mountcastle, John R. Thompson

Physics and Astronomy Faculty Scholarship

We report on several specific student difficulties regarding the second law of thermodynamics in the context of heat engines within upper-division undergraduate thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the second law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students’ struggles in reasoning about situations that are physically impossible …


Rényi Entanglement Entropy Of Critical Su(N) Spin Chains, Jonathan D'Emidio, Matthew S. Block, Ribhu K. Kaul Aug 2015

Rényi Entanglement Entropy Of Critical Su(N) Spin Chains, Jonathan D'Emidio, Matthew S. Block, Ribhu K. Kaul

Physics and Astronomy Faculty Publications

We present a study of the scaling behavior of the Rényi entanglement entropy (REE) in SU(N) spin chain Hamiltonians, in which all of the spins transform under the fundamental representation. These SU(N) spin chains are known to be quantum critical and described by a well known Wess-Zumino-Witten (WZW) nonlinear sigma model in the continuum limit. Numerical results from our lattice Hamiltonian are obtained using stochastic series expansion quantum Monte Carlo for both closed and open boundary conditions. As expected for this 1D critical system, the REE shows a logarithmic dependence on the subsystem size with a …


Lectures On Thermodynamics And Statistical Mechanics, V P. Nair Jan 2015

Lectures On Thermodynamics And Statistical Mechanics, V P. Nair

Open Educational Resources

No abstract provided.


Symmetry And The Order Of Events In Time: The Thermodynamics Of Blackbodies Composed Of Positive Or Negative Masssymmetry And The Order Of Events In Time: The Thermodynamics Of Blackbodies Composed Of Positive Or Negative Mass, Randy Wayne Jan 2015

Symmetry And The Order Of Events In Time: The Thermodynamics Of Blackbodies Composed Of Positive Or Negative Masssymmetry And The Order Of Events In Time: The Thermodynamics Of Blackbodies Composed Of Positive Or Negative Mass, Randy Wayne

Turkish Journal of Physics

I have previously proposed a discrete symmetry called CPM (charge-parity-mass) symmetry that defines matter as having positive mass and antimatter as having negative mass-both being involved in processes that proceed forward in time. I have generalized the second law of thermodynamics to describe and predict the order of events in time that take place in reversible thermodynamic systems composed of positive or negative mass. Here I extend the CPM symmetry to irreversible thermo-optical radiation systems characterized by the Stefan-Boltzmann law, Planck's blackbody radiation law, and Einstein's law of specific heat. The laws of radiation analyzed in terms of CPM symmetry …


Black Hole Microstates In String Theory, Joseph Lewkowicz Jan 2015

Black Hole Microstates In String Theory, Joseph Lewkowicz

Legacy Theses & Dissertations (2009 - 2024)

String theory has resolved the information paradox associated with entropy of black holes by identifying microscopic states contributing to this entropy. This thesis reviews the origin of the paradox, and discusses the progress in resolving it, starting from the counting of states by Strominger and Vafa, and culminating in the current work on constructing fuzzball geometries. A particular emphasis is given to a promising technique for constructing new geometries known as spectral flow.


Information-Entropic Measure Of Energy-Degenerate Kinks In Two-Field Models, R.A.C. Correa, A. De Souza Dutra, M. Gleiser Oct 2014

Information-Entropic Measure Of Energy-Degenerate Kinks In Two-Field Models, R.A.C. Correa, A. De Souza Dutra, M. Gleiser

Dartmouth Scholarship

We investigate the existence and properties of kink-like solitons in a class of models with two interacting scalar fields. In particular, we focus on models that display both double and single-kink solutions, treatable analytically using the Bogomol'nyi–Prasad–Sommerfield bound (BPS). Such models are of interest in applications that include Skyrmions and various superstring-motivated theories. Exploring a region of parameter space where the energy for very different spatially-bound configurations is degenerate, we show that a newly-proposed momentum–space entropic measure called Configurational Entropy (CE) can distinguish between such energy-degenerate spatial profiles. This information-theoretic measure of spatial complexity provides a complementary perspective to situations …


Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes Oct 2014

Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the …