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Schlenoff JB, Akkaoui K. Unifying the temperature dependent dynamics of glass formers. J Chem Phys 2024; 161:034502. [PMID: 39007391 DOI: 10.1063/5.0211693] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2024] [Accepted: 06/28/2024] [Indexed: 07/16/2024] Open
Abstract
Strong changes in bulk properties, such as modulus and viscosity, are observed near the glass transition temperature, Tg, of amorphous materials. For more than a century, intense efforts have been made to define a microscopic origin for these macroscopic changes in properties. Using transition state theory (TST), we delve into the atomic/molecular level picture of how microscopic localized unit relaxations, or "cage rattles," evolve to macroscopic structural relaxations above Tg. Unit motion is broken down into two populations: (1) simultaneous rearrangement occurs among a critical number of units, nα, which ranges from 1 to 4, allowing a systematic classification of glass formers, GFs, that is compared to fragility; and (2) near Tg, adjacent units provide additional free volume for rearrangement, not simultaneously, but within the "primitive" lifetime, τ1, of one unit rattling in its cage. Relaxation maps illustrate how Johari-Goldstein β-relaxations stem from the rattle of nα units. We analyzed a wide variety of glassy materials and materials with a glassy response using literature data. Our four-parameter equation fits "strong" and "weak" GFs over the entire range of temperatures and also extends to other glassy systems, such as ion-transporting polymers and ferroelectric relaxors. The role of activation entropy in boosting preexponential factors to high "unphysical" apparent frequencies is discussed. Enthalpy-entropy compensation is clearly illustrated using the TST approach.
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Affiliation(s)
- Joseph B Schlenoff
- Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Khalil Akkaoui
- Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, Florida 32306-4390, USA
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2
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Gavazzoni C, Brito C, Wyart M. Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules. PHYSICAL REVIEW LETTERS 2024; 132:248201. [PMID: 38949336 DOI: 10.1103/physrevlett.132.248201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Accepted: 04/23/2024] [Indexed: 07/02/2024]
Abstract
We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in which a fraction (1-f_{R}) of the particles can perform pairwise exchange or "swap moves," while a fraction f_{P} of the particles can move only along restricted directions. We find that (i) the location of the glass transition varies greatly but smoothly as f_{P} and f_{R} change and (ii) it is governed by a linear combination of f_{P} and f_{R}. (iii) Dynamical heterogeneities (DHs) are not governed by the static structure of the material; their magnitude correlates instead with the relaxation time. (iv) We show that a recent theory for temporal growth of DHs based on thermal avalanches holds quantitatively throughout the (f_{R},f_{P}) diagram. These observations are negative items for some existing theories of the glass transition, particularly those reliant on growing thermodynamic order or locally favored structure, and open new avenues to test other approaches, as we illustrate.
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Affiliation(s)
- Cristina Gavazzoni
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil
| | - Carolina Brito
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil
| | - Matthieu Wyart
- Institute of Physics, Ecole Polytechnique Federale de Lausanne, 729 BSP UNIL, 1015, Lausanne, Switzerland
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3
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Hasyim MR, Mandadapu KK. Emergent facilitation and glassy dynamics in supercooled liquids. Proc Natl Acad Sci U S A 2024; 121:e2322592121. [PMID: 38805280 PMCID: PMC11161792 DOI: 10.1073/pnas.2322592121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2023] [Accepted: 04/01/2024] [Indexed: 05/30/2024] Open
Abstract
In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic-subdiffusive-diffusive crossover MSD behaviors commonly found in supercooled liquids.
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Affiliation(s)
- Muhammad R. Hasyim
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA94720
| | - Kranthi K. Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA94720
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
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4
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Pica Ciamarra M, Ji W, Wyart M. Local vs. cooperative: Unraveling glass transition mechanisms with SEER. Proc Natl Acad Sci U S A 2024; 121:e2400611121. [PMID: 38787876 PMCID: PMC11145278 DOI: 10.1073/pnas.2400611121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2024] [Accepted: 04/17/2024] [Indexed: 05/26/2024] Open
Abstract
Which phenomenon slows down the dynamics in supercooled liquids and turns them into glasses is a long-standing question of condensed matter. Most popular theories posit that as the temperature decreases, many events must occur in a coordinated fashion on a growing length scale for relaxation to occur. Instead, other approaches consider that local barriers associated with the elementary rearrangement of a few particles or "excitations" govern the dynamics. To resolve this conundrum, our central result is to introduce an algorithm, Systematic Excitation ExtRaction, which can systematically extract hundreds of excitations and their energy from any given configuration. We also provide a measurement of the activation energy, characterizing the liquid dynamics, based on fast quenching and reheating. We use these two methods in a popular liquid model of polydisperse particles. Such polydisperse models are known to capture the hallmarks of the glass transition and can be equilibrated efficiently up to millisecond time scales. The analysis reveals that cooperative effects do not control the fragility of such liquids: the change of energy of local barriers determines the change of activation energy. More generally, these methods can now be used to measure the degree of cooperativity of any liquid model.
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Affiliation(s)
- Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
- Consiglio Nazionale delle Ricerce, CNR-SPIN, NapoliI-80126, Italy
| | - Wencheng Ji
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot76100, Israel
| | - Matthieu Wyart
- Institute of Physics, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
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5
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Dyre JC. Solid-that-Flows Picture of Glass-Forming Liquids. J Phys Chem Lett 2024; 15:1603-1617. [PMID: 38306474 PMCID: PMC10875679 DOI: 10.1021/acs.jpclett.3c03308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Revised: 01/12/2024] [Accepted: 01/17/2024] [Indexed: 02/04/2024]
Abstract
This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.
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Affiliation(s)
- Jeppe C Dyre
- "Glass and Time", IMFUFA, Dept. of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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6
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Saporta-Katz O, Moriel A. Self-driven configurational dynamics in frustrated spring-mass systems. Phys Rev E 2024; 109:024219. [PMID: 38491674 DOI: 10.1103/physreve.109.024219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 01/29/2024] [Indexed: 03/18/2024]
Abstract
Various physical systems relax mechanical frustration through configurational rearrangements. We examine such rearrangements via Hamiltonian dynamics of simple internally stressed harmonic four-mass systems. We demonstrate theoretically and numerically how mechanical frustration controls the underlying potential energy landscape. Then, we examine the harmonic four-mass systems' Hamiltonian dynamics and relate the onset of chaotic motion to self-driven rearrangements. We show such configurational dynamics may occur without strong precursors, rendering such dynamics seemingly spontaneous.
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Affiliation(s)
- Ori Saporta-Katz
- Computer Science and Applied Mathematics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Avraham Moriel
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
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7
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Ozawa M, Biroli G. Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids. PHYSICAL REVIEW LETTERS 2023; 130:138201. [PMID: 37067329 DOI: 10.1103/physrevlett.130.138201] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 03/02/2023] [Indexed: 06/19/2023]
Abstract
We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.
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Affiliation(s)
- Misaki Ozawa
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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8
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Lerbinger M, Barbot A, Vandembroucq D, Patinet S. Relevance of Shear Transformations in the Relaxation of Supercooled Liquids. PHYSICAL REVIEW LETTERS 2022; 129:195501. [PMID: 36399740 DOI: 10.1103/physrevlett.129.195501] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2021] [Revised: 07/18/2022] [Accepted: 10/09/2022] [Indexed: 06/16/2023]
Abstract
While deeply supercooled liquids exhibit divergent viscosity and increasingly heterogeneous dynamics as the temperature drops, their structure shows only seemingly marginal changes. Understanding the nature of relaxation processes in this dramatic slowdown is key for understanding the glass transition. Here, we show by atomistic simulations that the heterogeneous dynamics of glass-forming liquids strongly correlate with the local residual plastic strengths along soft directions computed in the initial inherent structures. The correlation increases with decreasing temperature and is maximum in the vicinity of the relaxation time. For the lowest temperature investigated, this maximum is comparable with the best values from the literature dealing with the structure-property relationship. However, the nonlinear probe of the local shear resistance in soft directions provides here a real-space picture of relaxation processes. Our detection method of thermal rearrangements allows us to investigate the first passage time statistics and to study the scaling between the activation energy barriers and the residual plastic strengths. These results shed new light on the nature of relaxations of glassy systems by emphasizing the analogy between the thermal relaxations in viscous liquids and the plastic shear transformation in amorphous solids.
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Affiliation(s)
- Matthias Lerbinger
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité, 75005 Paris, France
| | - Armand Barbot
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité, 75005 Paris, France
| | - Damien Vandembroucq
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité, 75005 Paris, France
| | - Sylvain Patinet
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité, 75005 Paris, France
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9
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Douglass IM, Dyre JC. Distance-as-time in physical aging. Phys Rev E 2022; 106:054615. [PMID: 36559484 DOI: 10.1103/physreve.106.054615] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 11/05/2022] [Indexed: 06/17/2023]
Abstract
Although it has been known for half a century that the physical aging of glasses in experiments is described well by a linear thermal-history convolution integral over the so-called material time, the microscopic definition and interpretation of the material time remains a mystery. We propose that the material-time increase over a given time interval reflects the distance traveled by the system's particles. Different possible distance measures are discussed, starting from the standard mean-square displacement and its inherent-state version that excludes the vibrational contribution. The viewpoint adopted, which is inspired by and closely related to pioneering works of Cugliandolo and Kurchan from the 1990s, implies a "geometric reversibility" and a "unique-triangle property" characterizing the system's path in configuration space during aging. Both of these properties are inherited from equilibrium, and they are here confirmed by computer simulations of an aging binary Lennard-Jones system. Our simulations moreover show that the slow particles control the material time. This motivates a "dynamic-rigidity-percolation" picture of physical aging. The numerical data show that the material time is dominated by the slowest particles' inherent mean-square displacement, which is conveniently quantified by the inherent harmonic mean-square displacement. This distance measure collapses data for potential-energy aging well in the sense that the normalized relaxation functions following different temperature jumps are almost the same function of the material time. Finally, the standard Tool-Narayanaswamy linear material-time convolution-integral description of physical aging is derived from the assumption that when time is replaced by distance in the above sense, an aging system is described by the same expression as that of linear-response theory.
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Affiliation(s)
- Ian M Douglass
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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10
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Lerner E, Bouchbinder E. Disordered Crystals Reveal Soft Quasilocalized Glassy Excitations. PHYSICAL REVIEW LETTERS 2022; 129:095501. [PMID: 36083650 DOI: 10.1103/physrevlett.129.095501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 08/04/2022] [Indexed: 06/15/2023]
Abstract
Structural glasses formed by quenching a melt are known to host a population of low-energy quasilocalized (nonphononic) excitations whose frequencies ω follow a universal ∼ω^{4} distribution as ω→0, independently of the glass formation history, the interparticle interaction potential, or spatial dimension. Here, we show that the universal quartic law of nonphononic excitations also holds in disordered crystals featuring finite long-range order, which is absent in their glassy counterparts. We thus establish that the degree of universality of the quartic law extends beyond structural glasses quenched from a melt. We further find that disordered crystals, whose level of disorder can be continuously controlled, host many more quasilocalized excitations than expected based on their degree of mechanical disorder-quantified by the relative fluctuations of the shear modulus-as compared to structural glasses featuring a similar degree of mechanical disorder. Our results are related to glasslike anomalies experimentally observed in disordered crystals. More broadly, they constitute an important step toward tracing the essential ingredients necessary for the emergence of universal nonphononic excitations in disordered solids.
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Affiliation(s)
- E Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - E Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
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11
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Sharma M, Nandi MK, Bhattacharyya SM. Identifying structural signature of dynamical heterogeneity via the local softness parameter. Phys Rev E 2022; 105:044604. [PMID: 35590668 DOI: 10.1103/physreve.105.044604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
In this work we study the relationship between the softness of a mean-field caging potential and dynamics at the local level. We first describe the local softness, which shows a distribution, thus identifying structural heterogeneity. We show that the lifetime of the softness parameter is connected to the lifetime of the well-known cage structure in supercooled liquids. Finally, our theory predicts that the local softness and the local dynamics is causal below the onset temperature where there is a decoupling between the short and long time dynamics, thus allowing a static description of the cage. With the decrease in temperature, the correlation between structure and dynamics increases. The study shows that at lower temperatures, the structural heterogeneity increases, and since the structure becomes a better predictor of the dynamics, it leads to an increase in the dynamical heterogeneity. We also find that the softness of a hard, immobile region evolves with time and becomes soft and eventually mobile due to the rearrangements in the neighborhood, confirming the well-known facilitation effect.
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Affiliation(s)
- Mohit Sharma
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune-411008, India
| | - Manoj Kumar Nandi
- Department of Engineering, University of Campania "Luigi Vanvitelli" 81031 Aversa (Caserta), Italy
| | - Sarika Maitra Bhattacharyya
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune-411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
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12
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Lerner E, Bouchbinder E. Low-energy quasilocalized excitations in structural glasses. J Chem Phys 2021; 155:200901. [PMID: 34852497 DOI: 10.1063/5.0069477] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective, we review developments over the past three decades toward understanding the emergence of QLEs in structural glasses and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.
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Affiliation(s)
- Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
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