1
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Di Terlizzi I, Gironella M, Herraez-Aguilar D, Betz T, Monroy F, Baiesi M, Ritort F. Variance sum rule for entropy production. Science 2024; 383:971-976. [PMID: 38422150 DOI: 10.1126/science.adh1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 01/09/2024] [Indexed: 03/02/2024]
Abstract
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.
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Affiliation(s)
- I Di Terlizzi
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - M Gironella
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Department of Medical Biochemistry and Cell Biology, Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, 40530 Gothenburg, Sweden
| | - D Herraez-Aguilar
- Facultad de Ciencias Experimentales, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - T Betz
- Third Institute of Physics, Georg August Universität Göttingen, Göttingen, Germany
- Cluster of Excellence "Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells" (MBExC), University of Göttingen, Göttingen, Germany
| | - F Monroy
- Departamento de Química Física, Facultad de Química, Universidad Complutense, 28040 Madrid, Spain
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía, 28041 Madrid, Spain
| | - M Baiesi
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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2
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Alston H, Cocconi L, Bertrand T. Irreversibility across a Nonreciprocal PT-Symmetry-Breaking Phase Transition. PHYSICAL REVIEW LETTERS 2023; 131:258301. [PMID: 38181344 DOI: 10.1103/physrevlett.131.258301] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 10/30/2023] [Indexed: 01/07/2024]
Abstract
Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time reversibility have so far been limited to microscopic models. Here, we derive a general expression for the average rate of informational entropy production in the most generic mixture of conserved phase fields with nonreciprocal couplings and additive conservative noise. For the particular case of a binary system with Cahn-Hilliard dynamics augmented by nonreciprocal cross-diffusion terms, we observe a nontrivial scaling of the entropy production rate across a parity-time symmetry breaking phase transition. We derive a closed-form analytic expression in the weak-noise regime for the entropy production rate due to the emergence of a macroscopic dynamic phase, showing it can be written in terms of the global polar order parameter, a measure of parity-time symmetry breaking.
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Affiliation(s)
- Henry Alston
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
| | - Luca Cocconi
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
- The Francis Crick Institute, London NW1 1AT, United Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Thibault Bertrand
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
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3
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Suchanek T, Kroy K, Loos SAM. Time-reversal and parity-time symmetry breaking in non-Hermitian field theories. Phys Rev E 2023; 108:064123. [PMID: 38243548 DOI: 10.1103/physreve.108.064123] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 11/06/2023] [Indexed: 01/21/2024]
Abstract
We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time (PT) symmetry-breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-Hermitian dynamics, namely, oscillatory instabilities and critical exceptional points, a low-noise expansion exposes a pretransitional surge of the mesoscale (informatic) entropy production rate, inside the static phases. Its scaling in the susceptibility contrasts conventional critical points (such as second-order phase transitions), where the susceptibility also diverges, but the entropy production generally remains finite. The difference can be attributed to active fluctuations in the wavelengths that become unstable. For critical exceptional points, we identify the coupling of eigenmodes as the entropy-generating mechanism, causing a drastic noise amplification in the Goldstone mode.
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Affiliation(s)
- Thomas Suchanek
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Klaus Kroy
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Sarah A M Loos
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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4
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Semeraro M, Gonnella G, Suma A, Zamparo M. Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle. PHYSICAL REVIEW LETTERS 2023; 131:158302. [PMID: 37897759 DOI: 10.1103/physrevlett.131.158302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 09/13/2023] [Indexed: 10/30/2023]
Abstract
We study the active work fluctuations of an active Ornstein-Uhlenbeck particle in the presence of a confining harmonic potential. We tackle the problem analytically both for stationary and generic uncorrelated initial states. Our results show that harmonic confinement can induce singularities in the active work rate function, with linear stretches at large positive and negative active work, at sufficiently large active and harmonic force constants. These singularities originate from big jumps in the displacement and in the active force, occurring at the initial or ending points of trajectories and marking the relevance of boundary terms in this problem.
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Affiliation(s)
- Massimiliano Semeraro
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Giuseppe Gonnella
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Antonio Suma
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Marco Zamparo
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
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5
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Caprini L, Marini Bettolo Marconi U, Löwen H. Entropy production and collective excitations of crystals out of equilibrium: The concept of entropons. Phys Rev E 2023; 108:044603. [PMID: 37978682 DOI: 10.1103/physreve.108.044603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2023] [Accepted: 09/21/2023] [Indexed: 11/19/2023]
Abstract
We study the collective vibrational excitations of crystals under out-of-equilibrium steady conditions that give rise to entropy production. Their excitation spectrum comprises equilibriumlike phonons of thermal origin and additional collective excitations called entropons because each of them represents a mode of spectral entropy production. Entropons coexist with phonons and dominate them when the system is far from equilibrium while they are negligible in near-equilibrium regimes. The concept of entropons has been recently introduced and verified in a special case of crystals formed by self-propelled particles. Here we show that entropons exist in a broader class of active crystals that are intrinsically out of equilibrium and characterized by the lack of detailed balance. After a general derivation, several explicit examples are discussed, including crystals consisting of particles with alignment interactions and frictional contact forces.
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Affiliation(s)
- L Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II: Weiche Materie, Universitätsstrasse, 40225 Düsseldorf, Germany
| | - U Marini Bettolo Marconi
- Physics Department, Scuola di Scienze e Tecnologie, Università di Camerino - via Madonna delle Carceri, 62032 Camerino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, 06123 Perugia, Italy
| | - H Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II: Weiche Materie, Universitätsstrasse, 40225 Düsseldorf, Germany
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6
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Caprini L, Marini Bettolo Marconi U, Puglisi A, Löwen H. Entropons as collective excitations in active solids. J Chem Phys 2023; 159:041102. [PMID: 37486049 DOI: 10.1063/5.0156312] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 07/05/2023] [Indexed: 07/25/2023] Open
Abstract
The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers.
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Affiliation(s)
- Lorenzo Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi-CNR and Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
- INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Hartmut Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
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7
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Hurtado-Gutiérrez R, Hurtado PI, Pérez-Espigares C. Spectral signatures of symmetry-breaking dynamical phase transitions. Phys Rev E 2023; 108:014107. [PMID: 37583207 DOI: 10.1103/physreve.108.014107] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 06/12/2023] [Indexed: 08/17/2023]
Abstract
Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete Z_{n} symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.
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Affiliation(s)
- R Hurtado-Gutiérrez
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - P I Hurtado
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - C Pérez-Espigares
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
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8
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Omar AK, Row H, Mallory SA, Brady JF. Mechanical theory of nonequilibrium coexistence and motility-induced phase separation. Proc Natl Acad Sci U S A 2023; 120:e2219900120. [PMID: 37094152 PMCID: PMC10160997 DOI: 10.1073/pnas.2219900120] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 03/24/2023] [Indexed: 04/26/2023] Open
Abstract
Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both nonequilibrium and equilibrium systems. Here, we present a general mechanical theory for phase separation rooted in ideas explored nearly a half-century ago in the study of inhomogeneous fluids. The core idea is that the mechanical forces within the interface separating two coexisting phases uniquely determine coexistence criteria, regardless of whether a system is in equilibrium or not. We demonstrate the power and utility of this theory by applying it to active Brownian particles, predicting a quantitative phase diagram for motility-induced phase separation in both two and three dimensions. This formulation additionally allows for the prediction of novel interfacial phenomena, such as an increasing interface width while moving deeper into the two-phase region, a uniquely nonequilibrium effect confirmed by computer simulations. The self-consistent determination of bulk phase behavior and interfacial phenomena offered by this mechanical perspective provide a concrete path forward toward a general theory for nonequilibrium phase transitions.
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Affiliation(s)
- Ahmad K. Omar
- Department of Materials Science and Engineering, University of California, Berkeley, CA94720
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
| | - Hyeongjoo Row
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA91125
| | - Stewart A. Mallory
- Department of Chemistry, The Pennsylvania State University, University Park, PA16802
| | - John F. Brady
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA91125
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9
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Omar AK, Klymko K, GrandPre T, Geissler PL, Brady JF. Tuning nonequilibrium phase transitions with inertia. J Chem Phys 2023; 158:074904. [PMID: 36813709 DOI: 10.1063/5.0138256] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.
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Affiliation(s)
- Ahmad K Omar
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
| | - Katherine Klymko
- NERSC, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - John F Brady
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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10
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Hecht L, Mandal S, Löwen H, Liebchen B. Active Refrigerators Powered by Inertia. PHYSICAL REVIEW LETTERS 2022; 129:178001. [PMID: 36332249 DOI: 10.1103/physrevlett.129.178001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Revised: 05/09/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
We present the operational principle for a refrigerator that uses inertial effects in active Brownian particles to locally reduce their (kinetic) temperature by 2 orders of magnitude below the environmental temperature. This principle exploits the peculiar but so-far unknown shape of the phase diagram of inertial active Brownian particles to initiate motility-induced phase separation in the targeted cooling regime only. Remarkably, active refrigerators operate without requiring isolating walls opening the route toward using them to systematically absorb and trap, e.g., toxic substances from the environment.
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Affiliation(s)
- Lukas Hecht
- Institut für Physik kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, D-64289 Darmstadt, Germany
| | - Suvendu Mandal
- Institut für Physik kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, D-64289 Darmstadt, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II-Soft Matter, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Benno Liebchen
- Institut für Physik kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, D-64289 Darmstadt, Germany
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11
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Lamtyugina A, Qiu Y, Fodor É, Dinner AR, Vaikuntanathan S. Thermodynamic Control of Activity Patterns in Cytoskeletal Networks. PHYSICAL REVIEW LETTERS 2022; 129:128002. [PMID: 36179154 PMCID: PMC10014041 DOI: 10.1103/physrevlett.129.128002] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Accepted: 07/26/2022] [Indexed: 06/16/2023]
Abstract
Biological materials, such as the actin cytoskeleton, exhibit remarkable structural adaptability to various external stimuli by consuming different amounts of energy. In this Letter, we use methods from large deviation theory to identify a thermodynamic control principle for structural transitions in a model cytoskeletal network. Specifically, we demonstrate that biasing the dynamics with respect to the work done by nonequilibrium components effectively renormalizes the interaction strength between such components, which can eventually result in a morphological transition. Our work demonstrates how a thermodynamic quantity can be used to renormalize effective interactions, which in turn can tune structure in a predictable manner, suggesting a thermodynamic principle for the control of cytoskeletal structure and dynamics.
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Affiliation(s)
| | - Yuqing Qiu
- Department of Chemistry, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Étienne Fodor
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Aaron R. Dinner
- Department of Chemistry, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Suriyanarayanan Vaikuntanathan
- Department of Chemistry, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
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12
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Yan J, Rotskoff G. Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control. J Chem Phys 2022; 157:074101. [DOI: 10.1063/5.0095593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a current or entropy production rate, has become a central problem in nonequilibrium statistical mechanics. Asymptotically, for a broad class of observables, the distribution of a given observable satisfies a large deviation principle when the dynamics is Markovian, meaning that fluctuations can be characterized in the long-time limit by computing a scaled cumulant generating function. Calculating this function is not tractable analytically (nor often numerically) for complex, interacting systems, so the development of robust numerical techniques to carry out this computation is needed to probe the properties of nonequilibrium materials. Here, we describe an algorithm that recasts this task as an optimal control problem that can be solved variationally. We solve for optimal control forces using neural network ansätze that are tailored to the physical systems to which the forces are applied. We demonstrate that this approach leads to transferable and accurate solutions in two systems featuring large numbers of interacting particles.
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Affiliation(s)
- Jiawei Yan
- Stanford University Department of Chemistry, United States of America
| | - Grant Rotskoff
- Chemistry, Stanford University Department of Chemistry, United States of America
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13
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Rassolov G, Tociu L, Fodor E, Vaikuntanathan S. From predicting to learning dissipation from pair correlations of active liquids. J Chem Phys 2022; 157:054901. [DOI: 10.1063/5.0097863] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. Towards designing such materials, an important challenge is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on these challenges. We first demonstrate analytically for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations which, unlike most existing approaches, is applicable even for strongly interacting particles and far from equilibrium, to predict dissipation in these systems. Based on this theory, we reveal analytically a robust relation between dissipation and structure which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network which maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out-of-equilibrium.
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Affiliation(s)
| | - Laura Tociu
- The University of Chicago, United States of America
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14
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Yan J, Touchette H, Rotskoff GM. Learning nonequilibrium control forces to characterize dynamical phase transitions. Phys Rev E 2022; 105:024115. [PMID: 35291069 DOI: 10.1103/physreve.105.024115] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem, based on importance sampling, cloning, and spectral approximations, have yielded significant insight into nonequilibrium systems but tend to scale poorly with the size of the system, especially near dynamical phase transitions. Here we propose a machine learning algorithm that samples rare trajectories and estimates the associated large deviation functions using a many-body control force by leveraging the flexible function representation provided by deep neural networks, importance sampling in trajectory space, and stochastic optimal control theory. We show that this approach scales to hundreds of interacting particles and remains robust at dynamical phase transitions.
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Affiliation(s)
- Jiawei Yan
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Hugo Touchette
- Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa
| | - Grant M Rotskoff
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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15
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Das A, Kuznets-Speck B, Limmer DT. Direct Evaluation of Rare Events in Active Matter from Variational Path Sampling. PHYSICAL REVIEW LETTERS 2022; 128:028005. [PMID: 35089729 DOI: 10.1103/physrevlett.128.028005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Accepted: 12/09/2021] [Indexed: 06/14/2023]
Abstract
Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogs, transformations between distinct metastable states in active matter proceed through rare fluctuations; however, their detailed balance violating dynamics renders these events difficult to study. Here, we present a simulation method for evaluating the rate and mechanism of rare events in generic nonequilibrium systems and apply it to study the conformational changes of a passive solute in an active fluid. The method employs a variational optimization of a control force that renders the rare event a typical one, supplying an exact estimate of its rate as a ratio of path partition functions. Using this method we find that increasing activity in the active bath can enhance the rate of conformational switching of the passive solute in a manner consistent with recent bounds from stochastic thermodynamics.
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Affiliation(s)
- Avishek Das
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawerence Berkeley National Laboratory, Berkeley, California 94720, USA
- Material Sciences Division, Lawerence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
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16
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Goswami K, Chakrabarti R. Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise. Phys Rev E 2021; 104:034113. [PMID: 34654068 DOI: 10.1103/physreve.104.034113] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 08/26/2021] [Indexed: 01/25/2023]
Abstract
We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a nonthermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in the case of a purely thermal bath, the distribution is double exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate, is investigated carefully. In addition, we study the first-arrival properties of the system in the presence of a delta-function sink with strength κ, where κ=0 and κ=∞ correspond to fully nonreactive and fully reactive sinks, respectively. We explore the effect of two competitive mechanisms: the diffusive spread in the presence of two noises and the increase in probability density around the initial position due to stochastic resetting. We show that there exists an optimal resetting rate, which minimizes the mean first-arrival time (MFAT) to the sink for a given value of the sink strength. We also explore the effect of the strength of the Poissonian noise on MFAT, in addition to sink strength. Our formalism generalizes the diffusion-limited reaction under resetting in a nonequilibrium bath and provides an efficient search strategy for a reactant to find a target site, relevant in a range of biophysical processes.
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Affiliation(s)
- Koushik Goswami
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Powai 400076, India
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Powai 400076, India
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17
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Das A, Rose DC, Garrahan JP, Limmer DT. Reinforcement learning of rare diffusive dynamics. J Chem Phys 2021; 155:134105. [PMID: 34624994 DOI: 10.1063/5.0057323] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a method to probe rare molecular dynamics trajectories directly using reinforcement learning. We consider trajectories that are conditioned to transition between regions of configuration space in finite time, such as those relevant in the study of reactive events, and trajectories exhibiting rare fluctuations of time-integrated quantities in the long time limit, such as those relevant in the calculation of large deviation functions. In both cases, reinforcement learning techniques are used to optimize an added force that minimizes the Kullback-Leibler divergence between the conditioned trajectory ensemble and a driven one. Under the optimized added force, the system evolves the rare fluctuation as a typical one, affording a variational estimate of its likelihood in the original trajectory ensemble. Low variance gradients employing value functions are proposed to increase the convergence of the optimal force. The method we develop employing these gradients leads to efficient and accurate estimates of both the optimal force and the likelihood of the rare event for a variety of model systems.
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Affiliation(s)
- Avishek Das
- Department of Chemistry, University of California, Berkeley, California 94609, USA
| | - Dominic C Rose
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94609, USA
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18
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A strong nonequilibrium bound for sorting of cross-linkers on growing biopolymers. Proc Natl Acad Sci U S A 2021; 118:2102881118. [PMID: 34518221 DOI: 10.1073/pnas.2102881118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/22/2021] [Indexed: 12/18/2022] Open
Abstract
Understanding the role of nonequilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and nonequilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle cross-linked by two competing types of actin-binding proteins [S. L. Freedman et al., Proc. Natl. Acad. Sci. U.S.A. 116, 16192-16197 (2019)], we construct a minimal model for such a system and show that the dynamics of a growing actin bundle are subject to a set of thermodynamic constraints that relate its nonequilibrium driving, morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes and offer a route to estimating microscopic driving forces from microscopy experiments.
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Lesnicki D, Gao CY, Limmer DT, Rotenberg B. On the molecular correlations that result in field-dependent conductivities in electrolyte solutions. J Chem Phys 2021; 155:014507. [PMID: 34241409 DOI: 10.1063/5.0052860] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Employing recent advances in response theory and nonequilibrium ensemble reweighting, we study the dynamic and static correlations that give rise to an electric field-dependent ionic conductivity in electrolyte solutions. We consider solutions modeled with both implicit and explicit solvents, with different dielectric properties, and at multiple concentrations. Implicit solvent models at low concentrations and small dielectric constants exhibit strongly field-dependent conductivities. We compare these results to Onsager-Wilson theory of the Wien effect, which provides a qualitatively consistent prediction at low concentrations and high static dielectric constants but is inconsistent away from these regimes. The origin of the discrepancy is found to be increased ion correlations under these conditions. Explicit solvent effects act to suppress nonlinear responses, yielding a weakly field-dependent conductivity over the range of physically realizable field strengths. By decomposing the relevant time correlation functions, we find that the insensitivity of the conductivity to the field results from the persistent frictional forces on the ions from the solvent. Our findings illustrate the utility of nonequilibrium response theory in rationalizing nonlinear transport behavior.
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Affiliation(s)
- Dominika Lesnicki
- Sorbonne Université, CNRS, Physico-Chimie des Electrolytes et Nanosystèmes Interfaciaux, Paris, France
| | - Chloe Y Gao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-Chimie des Electrolytes et Nanosystèmes Interfaciaux, Paris, France
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20
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Omar AK, Klymko K, GrandPre T, Geissler PL. Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation. PHYSICAL REVIEW LETTERS 2021; 126:188002. [PMID: 34018789 DOI: 10.1103/physrevlett.126.188002] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Revised: 03/06/2021] [Accepted: 04/05/2021] [Indexed: 06/12/2023]
Abstract
Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.
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Affiliation(s)
- Ahmad K Omar
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Katherine Klymko
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- NERSC, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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21
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Martin D, O'Byrne J, Cates ME, Fodor É, Nardini C, Tailleur J, van Wijland F. Statistical mechanics of active Ornstein-Uhlenbeck particles. Phys Rev E 2021; 103:032607. [PMID: 33862678 DOI: 10.1103/physreve.103.032607] [Citation(s) in RCA: 68] [Impact Index Per Article: 22.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.
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Affiliation(s)
- David Martin
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Jérémy O'Byrne
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Étienne Fodor
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Cesare Nardini
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Frédéric van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
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Keta YE, Fodor É, van Wijland F, Cates ME, Jack RL. Collective motion in large deviations of active particles. Phys Rev E 2021; 103:022603. [PMID: 33736055 DOI: 10.1103/physreve.103.022603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
We analyze collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyze the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.
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Affiliation(s)
- Yann-Edwin Keta
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Département de Physique, École normale supérieure de Lyon, 69364 Lyon Cedex 07, France
| | - Étienne Fodor
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Frédéric van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Michael E Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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