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Muenker TM, Knotz G, Krüger M, Betz T. Accessing activity and viscoelastic properties of artificial and living systems from passive measurement. NATURE MATERIALS 2024; 23:1283-1291. [PMID: 39085417 DOI: 10.1038/s41563-024-01957-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 06/26/2024] [Indexed: 08/02/2024]
Abstract
Living systems are complex dynamic entities that operate far from thermodynamic equilibrium. Their active, non-equilibrium behaviour requires energy to drive cellular organization and dynamics. Unfortunately, most statistical mechanics approaches are not valid in non-equilibrium situations, forcing researchers to use intricate and often invasive methods to study living processes. Here we experimentally demonstrate that an observable termed mean back relaxation quantifies the active mechanics of living cells from passively observed particle trajectories. The mean back relaxation represents the average trajectory of a particle after a recent motion and is calculated from three-point probabilities. We show that this parameter allows the detection of broken detailed balance in confined systems. We experimentally observe that it provides access to the non-equilibrium generating energy and viscoelastic properties of artificial bulk materials and living cells. These findings suggest that the mean back relaxation can function as a marker of non-equilibrium dynamics and is a non-invasive avenue to determine viscoelastic material properties from passive measurements.
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Affiliation(s)
- Till M Muenker
- Third Institute of Physics, Georg August Universität Göttingen, Göttingen, Germany
| | - Gabriel Knotz
- Institute of Theoretical Physics, Georg August Universität Göttingen, Göttingen, Germany
| | - Matthias Krüger
- Institute of Theoretical Physics, Georg August Universität Göttingen, Göttingen, Germany.
| | - Timo 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), Georg August Universität Göttingen, Göttingen, Germany.
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2
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Li Y, Li Z, Misra RP, Liang C, Gillen AJ, Zhao S, Abdullah J, Laurence T, Fagan JA, Aluru N, Blankschtein D, Noy A. Molecular transport enhancement in pure metallic carbon nanotube porins. NATURE MATERIALS 2024; 23:1123-1130. [PMID: 38937586 DOI: 10.1038/s41563-024-01925-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2023] [Accepted: 05/16/2024] [Indexed: 06/29/2024]
Abstract
Nanofluidic channels impose extreme confinement on water and ions, giving rise to unusual transport phenomena strongly dependent on the interactions at the channel-wall interface. Yet how the electronic properties of the nanofluidic channels influence transport efficiency remains largely unexplored. Here we measure transport through the inner pores of sub-1 nm metallic and semiconducting carbon nanotube porins. We find that water and proton transport are enhanced in metallic nanotubes over semiconducting nanotubes, whereas ion transport is largely insensitive to the nanotube bandgap value. Molecular simulations using polarizable force fields highlight the contributions of the anisotropic polarizability tensor of the carbon nanotubes to the ion-nanotube interactions and the water friction coefficient. We also describe the origin of the proton transport enhancement in metallic nanotubes using deep neural network molecular dynamics simulations. These results emphasize the complex role of the electronic properties of nanofluidic channels in modulating transport under extreme nanoscale confinement.
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Affiliation(s)
- Yuhao Li
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - Zhongwu Li
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - Rahul Prasanna Misra
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Chenxing Liang
- Walker Department of Mechanical Engineering, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA
| | - Alice J Gillen
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA
- Vivani Medical Inc., Emeryville, CA, USA
| | - Sidi Zhao
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA
- School of Engineering, University of California Merced, Merced, CA, USA
| | - Jobaer Abdullah
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA
- School of Natural Sciences, University of California Merced, Merced, CA, USA
| | - Ted Laurence
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - Jeffrey A Fagan
- Materials Science and Engineering Division, National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA
| | - Narayana Aluru
- Walker Department of Mechanical Engineering, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA.
| | - Daniel Blankschtein
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | - Aleksandr Noy
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA.
- School of Natural Sciences, University of California Merced, Merced, CA, USA.
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3
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Liang C, Aluru NR. Tuning Interfacial Water Friction through Moiré Twist. ACS NANO 2024; 18:16141-16150. [PMID: 38856748 DOI: 10.1021/acsnano.4c00733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2024]
Abstract
Foundations of nanofluidics can enable advances in diverse applications such as water desalination, energy harvesting, and biological analysis. Dynamically manipulating nanofluidic properties, such as diffusion and friction, is an area of great scientific interest. Twisted bilayer graphene, particularly at the magic angle, has garnered attention for its unconventional superconductivity and correlated insulator behavior due to strong electronic correlations. The impact of the electronic properties of moiré patterns in twisted bilayer graphene on structural and dynamic properties of water remains largely unexplored. Computational challenges, stemming from simulating large unit cells using density functional theory, have hindered progress. This study addresses this gap by investigating water behavior on twisted bilayer graphene, employing a deep neural network potential (DP) model trained with a data set from ab initio molecular dynamics simulations. It is found that as the twisted angle approaches the magic angle, interfacial water friction increases, leading to a reduced water diffusion. Notably, the analysis shows that at smaller twisted angles with larger moiré patterns, water is more likely to reside in AA stacking regions than AB (or BA) stacking regions, a distinction that diminishes with smaller moiré patterns. This study illustrates the potential for leveraging the distinctive properties of moiré systems to effectively control and optimize interfacial fluid behavior.
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Affiliation(s)
- Chenxing Liang
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Narayana R Aluru
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States
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4
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Ramesh VG, Peters KJH, Rodriguez SRK. Arcsine Laws of Light. PHYSICAL REVIEW LETTERS 2024; 132:133801. [PMID: 38613295 DOI: 10.1103/physrevlett.132.133801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2022] [Accepted: 02/06/2024] [Indexed: 04/14/2024]
Abstract
We demonstrate that the time-integrated light intensity transmitted by a coherently driven resonator obeys Lévy's arcsine laws-a cornerstone of extreme value statistics. We show that convergence to the arcsine distribution is algebraic, universal, and independent of nonequilibrium behavior due to nonconservative forces or nonadiabatic driving. We furthermore verify, numerically, that the arcsine laws hold in the presence of frequency noise and in Kerr-nonlinear resonators supporting non-Gaussian states. The arcsine laws imply a weak ergodicity breaking which can be leveraged to enhance the precision of resonant optical sensors with zero energy cost, as shown in our companion manuscript [V. G. Ramesh et al., companion paper, Phys. Rev. Res. (2024).PPRHAI2643-1564]. Finally, we discuss perspectives for probing the possible breakdown of the arcsine laws in systems with memory.
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Affiliation(s)
- V G Ramesh
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - K J H Peters
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - S R K Rodriguez
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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5
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Khali SS, Peruani F, Chaudhuri D. When an active bath behaves as an equilibrium one. Phys Rev E 2024; 109:024120. [PMID: 38491633 DOI: 10.1103/physreve.109.024120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 01/22/2024] [Indexed: 03/18/2024]
Abstract
Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity v_{0}. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as ∼v_{0}^{α} with 1<α<2. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.
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Affiliation(s)
| | - Fernando Peruani
- LPTM, CY Cergy Paris Université, 2 Avenue A. Chauvin, 95302 Cergy-Pontoise Cedex, France
| | - Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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6
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Das D, Pradhan P, Chatterjee S. Optimum transport in systems with time-dependent drive and short-ranged interactions. Phys Rev E 2023; 108:034107. [PMID: 37849159 DOI: 10.1103/physreve.108.034107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 08/14/2023] [Indexed: 10/19/2023]
Abstract
We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.
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Affiliation(s)
- Deepsikha Das
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Sakuntala Chatterjee
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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7
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Minoguchi M, Sasa SI. Divergent Stiffness of One-Dimensional Growing Interfaces. PHYSICAL REVIEW LETTERS 2023; 130:197101. [PMID: 37243631 DOI: 10.1103/physrevlett.130.197101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 01/12/2023] [Accepted: 04/13/2023] [Indexed: 05/29/2023]
Abstract
When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness.
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Affiliation(s)
| | - Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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8
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Chen Y, Wang X. Different effects of external force fields on aging Lévy walk. CHAOS (WOODBURY, N.Y.) 2023; 33:013102. [PMID: 36725624 DOI: 10.1063/5.0124654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Accepted: 12/06/2022] [Indexed: 06/18/2023]
Abstract
Aging phenomena have been observed in numerous physical systems. Many statistical quantities depend on the aging time ta for aging anomalous diffusion processes. This paper pays more attention to how an external force field affects the aging Lévy walk. Based on the Langevin picture of the Lévy walk and the generalized Green-Kubo formula, we investigate the quantities that include the ensemble- and time-averaged mean-squared displacements in both weak aging ta≪t and strong aging ta≫t cases and compare them to the ones in the absence of any force field. Two typical force fields, constant force F and time-dependent periodic force F(t)=f0sin(ωt), are considered for comparison. The generalized Einstein relation is also discussed in the case with the constant force. We find that the constant force is the key to causing the aging phenomena and enhancing the diffusion behavior of the aging Lévy walk, while the time-dependent periodic force is not. The different effects of the two kinds of forces on the aging Lévy walk are verified by both theoretical analyses and numerical simulations.
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Affiliation(s)
- Yao Chen
- College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China
| | - Xudong Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
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9
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Spiechowicz J, Marchenko IG, Hänggi P, Łuczka J. Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond. ENTROPY (BASEL, SWITZERLAND) 2022; 25:42. [PMID: 36673183 PMCID: PMC9857877 DOI: 10.3390/e25010042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 12/21/2022] [Accepted: 12/21/2022] [Indexed: 06/17/2023]
Abstract
The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
| | - Ivan G. Marchenko
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
- Kharkiv Institute of Physics and Technology, 61108 Kharkiv, Ukraine
- Education and Research Institute of Computer Physics and Energy, Karazin Kharkiv National University, 61022 Kharkiv, Ukraine
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
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10
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Sharma V, Tiwari S, Paul D, Sahu R, Chikkadi V, Kumar GVP. Optothermal pulling, trapping, and assembly of colloids using nanowire plasmons. SOFT MATTER 2021; 17:10903-10909. [PMID: 34807220 DOI: 10.1039/d1sm01365c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Optical excitation of colloids can be harnessed to realize soft matter systems that are out of equilibrium. In this paper, we present our experimental studies on the dynamics of silica colloids in the vicinity of a silver nanowire propagating surface plasmon polaritons (SPPs). Due to the optothermal interaction, the colloids are directionally pulled towards the excitation point of the nanowire. Having reached this point, they are spatio-temporally trapped around the excitation location. By increasing the concentration of colloids in the system, we observe multi-particle assembly around the nanowire. This process is thermophoretically driven and assisted by the SPPs. Furthermore, we find such an assembly to be sensitive to the excitation polarization at the input of the nanowire. Numerically-simulated temperature distribution around an illuminated nanowire corroborates sensitivity to the excitation polarization. Our study will find relevance in exploration of SPP-assisted optothermal pulling, trapping and assembly of colloids, and can serve as a test-bed of plasmon-driven active matter.
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Affiliation(s)
- Vandana Sharma
- Department of Physics, Indian Institute of Science Education and Research, Pune - 411008, India.
| | - Sunny Tiwari
- Department of Physics, Indian Institute of Science Education and Research, Pune - 411008, India.
| | - Diptabrata Paul
- Department of Physics, Indian Institute of Science Education and Research, Pune - 411008, India.
| | - Ratimanasee Sahu
- Department of Physics, Indian Institute of Science Education and Research, Pune - 411008, India.
| | - Vijayakumar Chikkadi
- Department of Physics, Indian Institute of Science Education and Research, Pune - 411008, India.
| | - G V Pavan Kumar
- Department of Physics, Indian Institute of Science Education and Research, Pune - 411008, India.
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11
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Jerez MJY, Bonachita MA, Confesor MNP. Reversibility in nonequilibrium steady states as a measure of distance from equilibrium. Phys Rev E 2021; 104:044609. [PMID: 34781472 DOI: 10.1103/physreve.104.044609] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Accepted: 09/29/2021] [Indexed: 11/07/2022]
Abstract
From the detailed balance-like relation, we propose a measure, K^{*}, of a nonequilibrium steady-state (NESS) distance from equilibrium. We investigate in particular the NESS of a particle confined in a time-dependent harmonic potential of constant stiffness but with an ON-OFF state following a telegraph process. Experimental results coupled with simulations show that K^{*} increases at slow switching rates (far from equilibrium) and approaches to zero at equilibrium conditions. Thus, the steady-state distribution together with K^{*} fully characterizes a NESS.
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Affiliation(s)
- Michael Jade Y Jerez
- Department of Physics and Complex Systems Group-PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Ave., Tibanga, Iligan City 9200, Philippines
| | - Mike A Bonachita
- Department of Physics and Complex Systems Group-PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Ave., Tibanga, Iligan City 9200, Philippines
| | - Mark Nolan P Confesor
- Department of Physics and Complex Systems Group-PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Ave., Tibanga, Iligan City 9200, Philippines
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12
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Asheichyk K, Fuchs M, Krüger M. Brownian systems perturbed by mild shear: comparing response relations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:405101. [PMID: 34139676 DOI: 10.1088/1361-648x/ac0c3c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 06/17/2021] [Indexed: 06/12/2023]
Abstract
We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.
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Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
- Department of Theoretical Physics and Astrophysics, Belarusian State University, 5 Babruiskaya St., 220006 Minsk, Belarus
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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13
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Wettstein A, Diddens D, Heuer A. Polymer Electrolytes in Strong External Electric Fields: Modification of Structure and Dynamics. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02385] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alina Wettstein
- Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, Corrensstraße 28/30, D-48149 Münster, Germany
| | - Diddo Diddens
- Institut für Energie- und Klimaforschung, Ionics in Energy Storage, Helmholtz Institut Münster, Forschungszentrum Jülich, Corrensstraße 46, 48149 Münster, Germany
| | - Andreas Heuer
- Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, Corrensstraße 28/30, D-48149 Münster, Germany
- Institut für Energie- und Klimaforschung, Ionics in Energy Storage, Helmholtz Institut Münster, Forschungszentrum Jülich, Corrensstraße 46, 48149 Münster, Germany
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14
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Xu Y, Liu X, Li Y, Metzler R. Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes. Phys Rev E 2021; 102:062106. [PMID: 33466052 DOI: 10.1103/physreve.102.062106] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 10/22/2020] [Indexed: 01/03/2023]
Abstract
Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent α. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent α is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.
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Affiliation(s)
- Yong Xu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.,MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China
| | - Xuemei Liu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Yongge Li
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.,Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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15
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Desgranges C, Delhommelle J. Entropy production in model colloidal suspensions under shear via the fluctuation theorem. J Chem Phys 2020; 153:224113. [DOI: 10.1063/5.0025954] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, New York University, New York, New York 10003, USA and Department of Chemistry & Molecular Simulation of NonEquilibrium Processes (MSNEP), Suite 2300, Tech Accelerator, University of North Dakota, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, New York University, New York, New York 10003, USA and Department of Chemistry & Molecular Simulation of NonEquilibrium Processes (MSNEP), Suite 2300, Tech Accelerator, University of North Dakota, Grand Forks, North Dakota 58202, USA
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16
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Tan X, Wang Y, Zhang Y, Wang M, Huo F, He H. Effect of Clusters on [Li] Solvation and Transport in Mixed Organic Compound/Ionic Liquid Electrolytes under External Electric Fields. Ind Eng Chem Res 2020. [DOI: 10.1021/acs.iecr.0c00296] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Xin Tan
- CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems, Beijing Key Laboratory of Ionic Liquids Clean Process, Institute of Process Engineering, Chinese Academy of Sciences, 1 North 2nd Street, Zhongguancun,
Haidian District, Beijing 100190, China
- School of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, 19A Yuquan Road, Shijingshan District, Beijing 100049, China
| | - Yanlei Wang
- CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems, Beijing Key Laboratory of Ionic Liquids Clean Process, Institute of Process Engineering, Chinese Academy of Sciences, 1 North 2nd Street, Zhongguancun,
Haidian District, Beijing 100190, China
| | - Yaqin Zhang
- CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems, Beijing Key Laboratory of Ionic Liquids Clean Process, Institute of Process Engineering, Chinese Academy of Sciences, 1 North 2nd Street, Zhongguancun,
Haidian District, Beijing 100190, China
| | - Meichen Wang
- CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems, Beijing Key Laboratory of Ionic Liquids Clean Process, Institute of Process Engineering, Chinese Academy of Sciences, 1 North 2nd Street, Zhongguancun,
Haidian District, Beijing 100190, China
| | - Feng Huo
- CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems, Beijing Key Laboratory of Ionic Liquids Clean Process, Institute of Process Engineering, Chinese Academy of Sciences, 1 North 2nd Street, Zhongguancun,
Haidian District, Beijing 100190, China
| | - Hongyan He
- CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Multiphase Complex Systems, Beijing Key Laboratory of Ionic Liquids Clean Process, Institute of Process Engineering, Chinese Academy of Sciences, 1 North 2nd Street, Zhongguancun,
Haidian District, Beijing 100190, China
- School of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, 19A Yuquan Road, Shijingshan District, Beijing 100049, China
- Zhengzhou Institute of Emerging Industrial Technology, Zhengzhou 450000, People’s Republic of China
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17
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Effective Equilibrium in Out-of-Equilibrium Interacting Coupled Nanoconductors. ENTROPY 2019; 22:e22010008. [PMID: 33285784 PMCID: PMC7516514 DOI: 10.3390/e22010008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/24/2019] [Revised: 12/07/2019] [Accepted: 12/11/2019] [Indexed: 11/25/2022]
Abstract
In the present work, we study a mesoscopic system consisting of a double quantum dot in which both quantum dots or artificial atoms are electrostatically coupled. Each dot is additionally tunnel coupled to two electronic reservoirs and driven far from equilibrium by external voltage differences. Our objective is to find configurations of these biases such that the current through one of the dots vanishes. In this situation, the validity of the fluctuation–dissipation theorem and Onsager’s reciprocity relations has been established. In our analysis, we employ a master equation formalism for a minimum model of four charge states, and limit ourselves to the sequential tunneling regime. We numerically study those configurations far from equilibrium for which we obtain a stalling current. In this scenario, we explicitly verify the fluctuation–dissipation theorem, as well as Onsager’s reciprocity relations, which are originally formulated for systems in which quantum transport takes place in the linear regime.
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18
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Drewsen M, Imparato A. Quantum duets working as autonomous thermal motors. Phys Rev E 2019; 100:042138. [PMID: 31770990 DOI: 10.1103/physreve.100.042138] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Indexed: 11/07/2022]
Abstract
We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks are shifted, the center of mass of the system exhibits a nonvanishing velocity, for which we provide an exact expression in the limit of small track undulations. We discuss the role of the broken spatial symmetry in the emergence of directed motion in thermal machines. We then consider the case in which external deterministic forces are applied to the system, and we characterize its steady-state velocity. If the applied external force opposes the system motion, work can be extracted from such a steady-state thermal machine, without any external cyclic protocol. When the two particles are not interacting, our results reduce to those of Fisher and Zwerger [Phys. Rev. B 32, 6190 (1985)PRBMDO0163-182910.1103/PhysRevB.32.6190] and Aslangul, Pottier, and Saint-James [J. Phys. France 48, 1093 (1987)JOPQAG0302-073810.1051/jphys:019870048070109300] for a single particle moving in a periodic tilted potential. We finally use our results for the motor velocity to check the validity of the quantum molecular dynamics algorithm in the nonlinear, nonequilibrium regime.
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Affiliation(s)
- Michael Drewsen
- Department of Physics and Astronomy, University of Aarhus Ny Munkegade, Building 1520, DK-8000 Aarhus C, Denmark
| | - Alberto Imparato
- Department of Physics and Astronomy, University of Aarhus Ny Munkegade, Building 1520, DK-8000 Aarhus C, Denmark
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19
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Oberreiter L, Seifert U, Barato AC. Subharmonic oscillations in stochastic systems under periodic driving. Phys Rev E 2019; 100:012135. [PMID: 31499923 DOI: 10.1103/physreve.100.012135] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Indexed: 06/10/2023]
Abstract
Subharmonic response is a well-known phenomenon in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics due to thermal fluctuations. In contrast to stochastic autonomous systems in a stationary state, for which the number of coherent oscillations is fundamentally bounded by the number of states in the underlying network, we demonstrate that in periodically driven systems, subharmonic oscillations can in principle remain coherent forever, even in networks with a small number of states. We also show that, inter alia, the thermodynamic cost rises only logarithmically with the number of coherent oscillations in a model calculation and that the possible periods of the persistent subharmonic response grow linearly with the number of states. We argue that our results can be relevant for biochemical oscillations and for stochastic models of time crystals.
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Affiliation(s)
- Lukas Oberreiter
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Andre C Barato
- Department of Physics, University of Houston, Houston, Texas 77204, USA
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20
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Asheichyk K, Solon AP, Rohwer CM, Krüger M. Response of active Brownian particles to shear flow. J Chem Phys 2019; 150:144111. [DOI: 10.1063/1.5086495] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kiryl Asheichyk
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
| | - Alexandre P. Solon
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matiére Condensée, LPTMC, F-75005 Paris, France
| | - Christian M. Rohwer
- 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
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21
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Abstract
The phenomena of subdiffusion are widely observed in physical and biological systems. To investigate the effects of external potentials, say, harmonic potential, linear potential, and time-dependent force, we study the subdiffusion described by the subordinated Langevin equation with white Gaussian noise or, equivalently, by the single Langevin equation with compound noise. If the force acts on the subordinated process, it keeps working all the time; otherwise, the force just exerts an influence on the system at the moments of jump. Some common statistical quantities, such as the ensemble- and time-averaged mean squared displacements, position autocorrelation function, correlation coefficient, and generalized Einstein relation, are discussed to distinguish the effects of various forces and different patterns of acting. The corresponding Fokker-Planck equations are also presented. All the stochastic processes discussed here are nonstationary, nonergodic, and aging.
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Affiliation(s)
- Yao Chen
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
| | - Xudong Wang
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
| | - Weihua Deng
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
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22
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Hou R, Cherstvy AG, Metzler R, Akimoto T. Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing. Phys Chem Chem Phys 2018; 20:20827-20848. [PMID: 30066003 DOI: 10.1039/c8cp01863d] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We demonstrate that in the presence of a drift CTRWs with α < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < α < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with α > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < α < 2 and α > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with α > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent α.
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Affiliation(s)
- Ru Hou
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
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23
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Cherstvy AG, Thapa S, Mardoukhi Y, Chechkin AV, Metzler R. Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity. Phys Rev E 2018; 98:022134. [PMID: 30253569 DOI: 10.1103/physreve.98.022134] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Indexed: 06/08/2023]
Abstract
How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and out-of-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.
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Affiliation(s)
- Andrey G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Samudrajit Thapa
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Yousof Mardoukhi
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Aleksei V Chechkin
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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24
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Rodrigo JA, Angulo M, Alieva T. Dynamic morphing of 3D curved laser traps for all-optical manipulation of particles. OPTICS EXPRESS 2018; 26:18608-18620. [PMID: 30114037 DOI: 10.1364/oe.26.018608] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2018] [Accepted: 05/29/2018] [Indexed: 06/08/2023]
Abstract
The development of optical manipulation techniques focused on the confinement and transport of micro/nano-particles has attracted increased interest in the last decades. In particular the combination of all-optical confinement and propelling forces, respectively arising from high intensity and phase gradients of a strongly focused laser beam, is promising for optical transport. The recently developed freestyle laser trap exploits this manipulation mechanism to achieve optical transport along arbitrary 3D curves. In practice, reconfigurable 3D optical transport of numerous particles is a challenging problem because it requires the ability to easily adapt the trajectory in real time. In this work, we introduce and experimentally demonstrate a strategy for on-task adaptive design of freestyle laser traps based on a dynamic morphing technique. This provides programmable smooth transformation of the 3D shape of the curved laser trap with independent control of the propelling forces along it, that can be configured according to the considered application. Dynamic morphing, proven here on the example of colloidal dielectric micro-particles, significantly simplifies the important problem of real-time reconfigurable 3D optical transport and opens up routes for other sophisticated optical manipulation tasks.
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25
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Huveneers F. Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment. Phys Rev E 2018; 97:042116. [PMID: 29758602 DOI: 10.1103/physreve.97.042116] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2017] [Indexed: 11/07/2022]
Abstract
We investigate the long-time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant D. We consider two cases: (a) The particle is pulled forward by a small external constant force and (b) there is no systematic bias. Theoretical arguments and numerical simulations provide evidence that the particle is eventually trapped by the environment. This is diagnosed in two ways: The asymptotic speed of the particle scales quadratically with the external force as it goes to zero, and the fluctuations scale diffusively in the unbiased environment, up to possible logarithmic corrections in both cases. Moreover, in the large D limit (homogenized regime), we find an important transient region giving rise to other, finite-size scalings, and we describe the crossover to the true asymptotic behavior.
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Affiliation(s)
- François Huveneers
- Université Paris-Dauphine, PSL Research University, CNRS, CEREMADE, 75016 Paris, France
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26
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Basu U, Helden L, Krüger M. Extrapolation to Nonequilibrium from Coarse-Grained Response Theory. PHYSICAL REVIEW LETTERS 2018; 120:180604. [PMID: 29775331 DOI: 10.1103/physrevlett.120.180604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Revised: 02/12/2018] [Indexed: 06/08/2023]
Abstract
Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.
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Affiliation(s)
- Urna Basu
- SISSA-International School for Advanced Studies and INFN, 34136 Trieste, Italy
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Laurent Helden
- 2. Physikalisches Institut, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Matthias Krüger
- 4th Institute for Theoretical Physics, Universität Stuttgart, 70550 Stuttgart, Germany
- Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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27
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Fischer LP, Pietzonka P, Seifert U. Large deviation function for a driven underdamped particle in a periodic potential. Phys Rev E 2018; 97:022143. [PMID: 29548104 DOI: 10.1103/physreve.97.022143] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2017] [Indexed: 11/07/2022]
Abstract
Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one-dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived, motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.
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Affiliation(s)
- Lukas P Fischer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Patrick Pietzonka
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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28
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Marsland R, England J. Limits of predictions in thermodynamic systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:016601. [PMID: 28976362 DOI: 10.1088/1361-6633/aa9101] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The past twenty years have seen a resurgence of interest in nonequilibrium thermodynamics, thanks to advances in the theory of stochastic processes and in their thermodynamic interpretation. Fluctuation theorems provide fundamental constraints on the dynamics of systems arbitrarily far from thermal equilibrium. Thermodynamic uncertainty relations bound the dissipative cost of precision in a wide variety of processes. Concepts of excess work and excess heat provide the basis for a complete thermodynamics of nonequilibrium steady states, including generalized Clausius relations and thermodynamic potentials. But these general results carry their own limitations: fluctuation theorems involve exponential averages that can depend sensitively on unobservably rare trajectories; steady-state thermodynamics makes use of a dual dynamics that lacks any direct physical interpretation. This review aims to present these central results of contemporary nonequilibrium thermodynamics in such a way that the power of each claim for making physical predictions can be clearly assessed, using examples from current topics in soft matter and biophysics.
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29
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Das A, Kundu A, Pradhan P. Einstein relation and hydrodynamics of nonequilibrium mass transport processes. Phys Rev E 2017; 95:062128. [PMID: 28709216 DOI: 10.1103/physreve.95.062128] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Indexed: 06/07/2023]
Abstract
We derive hydrodynamics of paradigmatic conserved-mass transport processes on a ring. The systems, governed by chipping, diffusion, and coalescence of masses, eventually reach a nonequilibrium steady state, having nontrivial correlations, with steady-state measures in most cases not known. In these processes, we analytically calculate two transport coefficients, bulk-diffusion coefficient and conductivity. Remarkably, the two transport coefficients obey an equilibrium-like Einstein relation even when the microscopic dynamics violates detailed balance and systems are far from equilibrium. Moreover, we show, using a macroscopic fluctuation theory, that the probability of large deviation in density, obtained from the above hydrodynamics, is in complete agreement with the same derived earlier by Das et al. [Phys. Rev. E 93, 062135 (2016)2470-004510.1103/PhysRevE.93.062135] using an additivity property.
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Affiliation(s)
- Arghya Das
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Anupam Kundu
- International Centre for Theoretical Sciences, TIFR, Bangalore 560012, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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30
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Krüger M, Maes C. The modified Langevin description for probes in a nonlinear medium. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:064004. [PMID: 28002047 DOI: 10.1088/1361-648x/29/6/064004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe's effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is no longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.
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Affiliation(s)
- Matthias Krüger
- 4th Institute for Theoretical Physics, Universität Stuttgart, Stuttgart, Germany. Max Planck Institute for Intelligent Systems, Stuttgart, Germany
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31
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Altaner B, Polettini M, Esposito M. Fluctuation-Dissipation Relations Far from Equilibrium. PHYSICAL REVIEW LETTERS 2016; 117:180601. [PMID: 27835007 DOI: 10.1103/physrevlett.117.180601] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2016] [Indexed: 06/06/2023]
Abstract
Near equilibrium, where all currents of a system vanish on average, the fluctuation-dissipation relation (FDR) connects a current's spontaneous fluctuations with its response to perturbations of the conjugate thermodynamic force. Out of equilibrium, fluctuation-response relations generally involve additional nondissipative contributions. Here, in the framework of stochastic thermodynamics, we show that an equilibriumlike FDR holds for internally equilibrated currents, if the perturbing conjugate force only affects the microscopic transitions that contribute to the current. We discuss the physical requirements for the validity of our result and apply it to nanosized electronic devices.
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Affiliation(s)
- Bernhard Altaner
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
| | - Matteo Polettini
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
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32
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Speck T. Thermodynamic formalism and linear response theory for nonequilibrium steady states. Phys Rev E 2016; 94:022131. [PMID: 27627270 DOI: 10.1103/physreve.94.022131] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Indexed: 11/07/2022]
Abstract
We study the linear response in systems driven away from thermal equilibrium into a nonequilibrium steady state with nonvanishing entropy production rate. A simple derivation of a general response formula is presented under the condition that the generating function describes a transformation that (to lowest order) preserves normalization and thus describes a physical stochastic process. For Markov processes we explicitly construct the conjugate quantities and discuss their relation with known response formulas. Emphasis is put on the formal analogy with thermodynamic potentials and some consequences are discussed.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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33
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Tsobgni Nyawo P, Touchette H. Large deviations of the current for driven periodic diffusions. Phys Rev E 2016; 94:032101. [PMID: 27739773 DOI: 10.1103/physreve.94.032101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2016] [Indexed: 06/06/2023]
Abstract
We study the large deviations of the time-integrated current for a driven diffusion on the circle, often used as a model of nonequilibrium systems. We obtain the large deviation functions describing the current fluctuations using a Fourier-Bloch decomposition of the so-called tilted generator, and we also construct from this decomposition the effective (biased, auxiliary, or driven) Markov process describing the diffusion as current fluctuations are observed in time. This effective process provides a clear physical explanation of the various fluctuation regimes observed. It is used here to obtain an upper bound on the current large deviation function, which we compare to a recently derived entropic bound, and to study the low-noise limit of large deviations.
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Affiliation(s)
- Pelerine Tsobgni Nyawo
- Institute of Theoretical Physics, Department of Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
| | - Hugo Touchette
- Institute of Theoretical Physics, Department of Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
- National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa
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34
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Chatterjee R, Chatterjee S, Pradhan P. Symmetric exclusion processes on a ring with moving defects. Phys Rev E 2016; 93:062124. [PMID: 27415225 DOI: 10.1103/physreve.93.062124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Indexed: 11/07/2022]
Abstract
We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders-a generalization of the model we proposed earlier [Phys. Rev. E 89, 022138 (2014)PLEEE81539-375510.1103/PhysRevE.89.022138]. The defects move with uniform velocity and change the particle hopping rates locally. We explore the collective effects of the defects on the spatial structure and transport properties of the system. We also introduce an SSEP with ordered sequential (sitewise) update and elucidate the close connection with our model.
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Affiliation(s)
- Rakesh Chatterjee
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
| | - Sakuntala Chatterjee
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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35
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Juniper MPN, Straube AV, Aarts DGAL, Dullens RPA. Colloidal particles driven across periodic optical-potential-energy landscapes. Phys Rev E 2016; 93:012608. [PMID: 26871123 DOI: 10.1103/physreve.93.012608] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2015] [Indexed: 11/07/2022]
Abstract
We study the motion of colloidal particles driven by a constant force over a periodic optical potential energy landscape. First, the average particle velocity is found as a function of the driving velocity and the wavelength of the optical potential energy landscape. The relationship between average particle velocity and driving velocity is found to be well described by a theoretical model treating the landscape as sinusoidal, but only at small trap spacings. At larger trap spacings, a nonsinusoidal model for the landscape must be used. Subsequently, the critical velocity required for a particle to move across the landscape is determined as a function of the wavelength of the landscape. Finally, the velocity of a particle driven at a velocity far exceeding the critical driving velocity is examined. Both of these results are again well described by the two theoretical routes for small and large trap spacings, respectively. Brownian motion is found to have a significant effect on the critical driving velocity but a negligible effect when the driving velocity is high.
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Affiliation(s)
- Michael P N Juniper
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, United Kingdom
| | - Arthur V Straube
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, United Kingdom
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, United Kingdom
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36
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Guérin T, Dean DS. Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062103. [PMID: 26764628 DOI: 10.1103/physreve.92.062103] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Indexed: 06/05/2023]
Abstract
We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.
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Affiliation(s)
- T Guérin
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux, F-33400 Talence, France
| | - D S Dean
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux, F-33400 Talence, France
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37
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Basu U, Krüger M, Lazarescu A, Maes C. Frenetic aspects of second order response. Phys Chem Chem Phys 2015; 17:6653-66. [DOI: 10.1039/c4cp04977b] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A theoretical framework to compute the second order response around equilibrium is provided and the importance of the so called frenetic contribution is illustrated.
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Affiliation(s)
- Urna Basu
- Instituut voor Theoretische Fysica
- KU Leuven
- Belgium
| | - Matthias Krüger
- 4th Institute for Theoretical Physics
- Universität Stuttgart, and Max Planck Institute for Intelligent Systems
- Stuttgart
- Germany
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38
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Hurowitz D, Cohen D. Nonequilibrium version of the Einstein relation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032129. [PMID: 25314417 DOI: 10.1103/physreve.90.032129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2014] [Indexed: 06/04/2023]
Abstract
The celebrated Einstein relation between the diffusion coefficient D and the drift velocity v is violated in nonequilibrium circumstances. We analyze how this violation emerges for the simplest example of a Brownian motion on a lattice, taking into account the interplay between the periodicity, the randomness, and the asymmetry of the transition rates. Based on the nonequilibrium fluctuation theorem the v/D ratio is found to be a nonlinear function of the affinity. Hence it depends in a nontrivial way on the microscopics of the sample.
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Affiliation(s)
- Daniel Hurowitz
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Doron Cohen
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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39
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Chaudhuri D. Active Brownian particles: entropy production and fluctuation response. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022131. [PMID: 25215712 DOI: 10.1103/physreve.90.022131] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2014] [Indexed: 06/03/2023]
Abstract
Within the Rayleigh-Helmholtz model of active Brownian particles, activity is due to a nonlinear velocity-dependent force. In the presence of external trapping potential or constant force, the steady state of the system breaks detailed balance producing a net entropy. Using molecular dynamics simulations, we obtain the probability distributions of entropy production in these steady states. The distribution functions obey fluctuation theorems for entropy production. Using the simulation, we further show that the steady-state response function obeys a modified fluctuation-dissipation relation.
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Affiliation(s)
- Debasish Chaudhuri
- Indian Institute of Technology Hyderabad, Yeddumailaram 502205, Andhra Pradesh, India
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40
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Chatterjee R, Chatterjee S, Pradhan P, Manna SS. Interacting particles in a periodically moving potential: traveling wave and transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022138. [PMID: 25353453 DOI: 10.1103/physreve.89.022138] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2013] [Indexed: 06/04/2023]
Abstract
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles where the diffusion dynamics is locally modified at a uniformly moving defect site, mimicking the effect of the periodically moving external potential. The model, though simple, exhibits remarkably rich features in particle transport, such as polarity reversal and double peaks in particle current upon variation of defect velocity and particle density. By tuning these variables, the most efficient transport can be achieved in either direction along the ring. These features can be understood in terms of a traveling density wave propagating in the system. Our results could be experimentally tested, e.g., in a system of colloidal particles driven by a moving optical tweezer.
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Affiliation(s)
- Rakesh Chatterjee
- CMP Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India
| | - Sakuntala Chatterjee
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
| | - S S Manna
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
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41
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Chakrabarty A, Konya A, Wang F, Selinger JV, Sun K, Wei QH. Brownian motion of boomerang colloidal particles. PHYSICAL REVIEW LETTERS 2013; 111:160603. [PMID: 24182246 DOI: 10.1103/physrevlett.111.160603] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Revised: 08/02/2013] [Indexed: 05/16/2023]
Abstract
We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.
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Affiliation(s)
- Ayan Chakrabarty
- Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
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42
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Noh JD, Kwon C, Park H. Multiple dynamic transitions in nonequilibrium work fluctuations. PHYSICAL REVIEW LETTERS 2013; 111:130601. [PMID: 24116762 DOI: 10.1103/physrevlett.111.130601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2013] [Revised: 01/07/2013] [Indexed: 06/02/2023]
Abstract
The time-dependent work probability distribution function P(W) is investigated analytically for a diffusing particle trapped by an anisotropic harmonic potential and driven by a nonconservative drift force in two dimensions. We find that the exponential tail shape of P(W) characterizing rare-event probabilities undergoes a sequence of dynamic transitions in time. These remarkable locking-unlocking type transitions result from an intricate interplay between a rotational mode induced by the nonconservative force and an anisotropic decaying mode due to the conservative attractive force. We expect that most of the high-dimensional dynamical systems should exhibit similar multiple dynamic transitions.
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Affiliation(s)
- Jae Dong Noh
- Department of Physics, University of Seoul, Seoul 130-743, Korea and School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
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43
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Chetrite R, Touchette H. Nonequilibrium microcanonical and canonical ensembles and their equivalence. PHYSICAL REVIEW LETTERS 2013; 111:120601. [PMID: 24093237 DOI: 10.1103/physrevlett.111.120601] [Citation(s) in RCA: 60] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2013] [Revised: 08/05/2013] [Indexed: 06/02/2023]
Abstract
Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here, we propose a theory of these ensembles that unifies and generalizes earlier results and show how it is fundamentally related to the large deviation properties of nonequilibrium systems. Using this theory, we provide conditions for the equivalence of nonequilibrium ensembles, generalizing those found for equilibrium systems, construct driven physical processes that generate these ensembles, and rederive in a simple way known and new product rules for their transition rates. A nonequilibrium diffusion model is used to illustrate these results.
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Affiliation(s)
- Raphaël Chetrite
- Laboratoire J. A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, Nice 06108, France
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44
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Ganguly C, Chaudhuri D. Stochastic thermodynamics of active Brownian particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032102. [PMID: 24125209 DOI: 10.1103/physreve.88.032102] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2013] [Indexed: 06/02/2023]
Abstract
Examples of self-propulsion in strongly fluctuating environments are abundant in nature, e.g., molecular motors and pumps operating in living cells. Starting from the Langevin equation of motion, we develop a stochastic thermodynamic description of noninteracting self-propelled particles using simple models of velocity-dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation-dissipation relation, characterizing the linear response in nonequilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot models of self-propelled particles.
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Affiliation(s)
- Chandrima Ganguly
- Indian Institute of Technology Hyderabad, Yeddumailaram 502205, Andhra Pradesh, India
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45
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Shi R, Wang Y. Ion-Cage Interpretation for the Structural and Dynamic Changes of Ionic Liquids under an External Electric Field. J Phys Chem B 2013; 117:5102-12. [DOI: 10.1021/jp311017r] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Rui Shi
- State Key Laboratory of Theoretical
Physics, Institute
of Theoretical Physics, Chinese Academy of Sciences, 55 East Zhongguancun Road, P.O. Box 2735, Beijing 100190, China
| | - Yanting Wang
- State Key Laboratory of Theoretical
Physics, Institute
of Theoretical Physics, Chinese Academy of Sciences, 55 East Zhongguancun Road, P.O. Box 2735, Beijing 100190, China
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46
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Ladadwa I, Heuer A. Nonlinear response and crowding effects in microrheology. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012302. [PMID: 23410326 DOI: 10.1103/physreve.87.012302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2012] [Revised: 10/31/2012] [Indexed: 06/01/2023]
Abstract
The mobility of tagged particles in a microrheological setup has been investigated via molecular dynamics simulations of a three-dimensional Lennard-Jones binary mixture. After coupling a small number of particles to a constant external driving force, the drift velocity and other observables of the dragged probe particles are reported in the linear and nonlinear response regime. In the nonlinear regime significant crowding effects are observed, thereby creating stringlike structures. Formation of the strings further enhances the nonlinear effects. A systematic study of these effects' dependence on temperature and total number of driven probe atoms is presented.
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Affiliation(s)
- I Ladadwa
- Westfälische Wilhelms-Universität Münster, Institut für physikalische Chemie, Corrensstrasse 30, 48149 Münster, Germany.
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47
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Seifert U. Stochastic thermodynamics, fluctuation theorems and molecular machines. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:126001. [PMID: 23168354 DOI: 10.1088/0034-4885/75/12/126001] [Citation(s) in RCA: 1198] [Impact Index Per Article: 99.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
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Affiliation(s)
- Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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48
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Nemoto T. Zon-Cohen singularity and negative inverse temperature in a trapped-particle limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061124. [PMID: 23005068 DOI: 10.1103/physreve.85.061124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2012] [Indexed: 06/01/2023]
Abstract
We study a Brownian particle on a moving periodic potential. We focus on the statistical properties of the work done by the potential and the heat dissipated by the particle. When the period and the depth of the potential are both large, by using a boundary layer analysis, we calculate a cumulant generating function and a biased distribution function. The result allows us to understand a Zon-Cohen singularity for an extended fluctuation theorem from a viewpoint of rare trajectories characterized by a negative inverse temperature of the biased distribution function.
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Affiliation(s)
- Takahiro Nemoto
- Department of Basic Science, The University of Tokyo, Tokyo, 153-8902, Japan
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49
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Lander B, Seifert U, Speck T. Effective confinement as origin of the equivalence of kinetic temperature and fluctuation-dissipation ratio in a dense shear-driven suspension. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021103. [PMID: 22463149 DOI: 10.1103/physreve.85.021103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2011] [Indexed: 05/31/2023]
Abstract
We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow.
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Affiliation(s)
- Boris Lander
- II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, DE-70550 Stuttgart, Germany
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50
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Abreu D, Seifert U. Thermodynamics of genuine nonequilibrium states under feedback control. PHYSICAL REVIEW LETTERS 2012; 108:030601. [PMID: 22400724 DOI: 10.1103/physrevlett.108.030601] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2011] [Indexed: 05/31/2023]
Abstract
For genuine nonequilibrium states that even at fixed external control parameter exhibit dissipation, we extend the Hatano-Sasa equality to processes with feedback control. The resulting bound on the maximal extractable work is substantially sharper than what would follow from applying the Sagawa-Ueda equality to transitions involving such states. For repeated measurements at short enough intervals, the power thus extracted can even exceed the average cost of driving as demonstrated explicitly with a simple, analytically solvable example.
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Affiliation(s)
- David Abreu
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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