1
|
Caspers J, Krüger M. Nonlinear Langevin functionals for a driven probe. J Chem Phys 2024; 161:124109. [PMID: 39319648 DOI: 10.1063/5.0227674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2024] [Accepted: 09/04/2024] [Indexed: 09/26/2024] Open
Abstract
When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism. (i) For a particle driven with the prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. (ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third- or second-order response, respectively.
Collapse
Affiliation(s)
- Juliana Caspers
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
| |
Collapse
|
2
|
Silvano N, Barci DG. Emergent gauge symmetry in active Brownian matter. Phys Rev E 2024; 109:044605. [PMID: 38755850 DOI: 10.1103/physreve.109.044605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 04/04/2024] [Indexed: 05/18/2024]
Abstract
We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).
Collapse
Affiliation(s)
- Nathan Silvano
- Center for Advanced Systems Understanding, Untermarkt 20, 02826 Görlitz, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
| | - Daniel G Barci
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
| |
Collapse
|
3
|
Wiese R, Kroy K, Levis D. Fluid-Glass-Jamming Rheology of Soft Active Brownian Particles. PHYSICAL REVIEW LETTERS 2023; 131:178302. [PMID: 37955492 DOI: 10.1103/physrevlett.131.178302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 09/13/2023] [Accepted: 10/03/2023] [Indexed: 11/14/2023]
Abstract
We numerically study the shear rheology of a binary mixture of soft active Brownian particles, from the fluid to the disordered solid regime. At low shear rates, we find a Newtonian regime, where a Green-Kubo relation with an effective temperature provides the linear viscosity. It is followed by a shear-thinning regime at high shear rates. At high densities, solidification is signaled by the emergence of a finite yield stress. We construct a "fluid-glass-jamming" phase diagram with activity replacing temperature. While both parameters gauge fluctuations, activity also changes the exponent characterizing the decay of the diffusivity close to the glass transition and the shape of the yield stress surface. The dense disordered active solid appears to be mostly dominated by athermal jamming rather than glass rheology.
Collapse
Affiliation(s)
- Roland Wiese
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
| | - Klaus Kroy
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
| | - Demian Levis
- Departement de Física de la Materia Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
- University of Barcelona Institute of Complex Systems (UBICS), Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| |
Collapse
|
4
|
Chun HM, Horowitz JM. Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks. J Chem Phys 2023; 158:2888610. [PMID: 37144710 DOI: 10.1063/5.0148662] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 04/17/2023] [Indexed: 05/06/2023] Open
Abstract
We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number fluctuations and the maximum thermodynamic driving force. We prove these trade-offs for linear chemical reaction networks and a class of nonlinear chemical reaction networks with a single chemical species. Numerical results for several model systems support the conclusion that these trade-offs continue to hold for a broad class of chemical reaction networks, though their precise form appears to sensitively depend on the deficiency of the network.
Collapse
Affiliation(s)
- Hyun-Myung Chun
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Jordan M Horowitz
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| |
Collapse
|
5
|
Anand SK, Singh SP. Migration of active filaments under Poiseuille flow in a microcapillary tube. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:150. [PMID: 34910263 DOI: 10.1140/epje/s10189-021-00153-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 11/20/2021] [Indexed: 06/14/2023]
Abstract
We present a comprehensive study of active filaments confined in a cylindrical channel under Poiseuille flow. The activity drives the filament towards the channel boundary, whereas external fluid flow migrates the filament away from the boundary. This migration further shifts towards the centre for higher flow strength. The migration behaviour of the filaments is presented in terms of the alignment order parameter that shows the alignment grows with shear and activity. Further, we have also addressed the role of length of filament on the migration behaviour, which suggests higher migration for larger filaments. Moreover, we discuss the polar ordering of filaments as a function of distance from the centre of channel that displays upstream motion near the boundary and downstream motion at the centre of the tube.
Collapse
Affiliation(s)
- Shalabh K Anand
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh, 462066, India
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh, 462066, India.
| |
Collapse
|
6
|
Baldovin M, Caprini L, Vulpiani A. Handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics. Phys Rev E 2021; 104:L032101. [PMID: 34654124 DOI: 10.1103/physreve.104.l032101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Accepted: 07/17/2021] [Indexed: 11/07/2022]
Abstract
We introduce a general formulation of the fluctuation-dissipation relations (FDRs) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require explicit knowledge of the stationary probability density function. Our formula applies to Markov stochastic systems with generic noise distributions: When the noise is additive and Gaussian, the relation reduces to those known in the literature; for multiplicative and non-Gaussian distributions (e.g., Cauchy noise) it provides exact results in agreement with numerical simulations. Our formula allows us to reproduce, in a suitable small-noise limit, the response functions of deterministic, strongly nonlinear dynamical models, even in the presence of chaotic behavior: This could have important practical applications in several contexts, including geophysics and climate. As a case of study, we consider the Lorenz '63 model, which is paradigmatic for the chaotic properties of deterministic dynamical systems.
Collapse
Affiliation(s)
- M Baldovin
- Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - L Caprini
- Scuola di Scienze e Tecnologie, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy
| | - A Vulpiani
- Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy
| |
Collapse
|
7
|
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.
Collapse
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
| |
Collapse
|
8
|
Bae Y, Lee S, Kim J, Jeong H. Inertial effects on the Brownian gyrator. Phys Rev E 2021; 103:032148. [PMID: 33862720 DOI: 10.1103/physreve.103.032148] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 02/18/2021] [Indexed: 11/07/2022]
Abstract
The recent interest into the Brownian gyrator has been confined chiefly to the analysis of Brownian dynamics both in theory and experiment despite the applicability of general cases with definite mass. Considering mass explicitly in the solution of the Fokker-Planck equation and Langevin dynamics simulations, we investigate how inertia can change the dynamics and energetics of the Brownian gyrator. In the Langevin model, the inertia reduces the nonequilibrium effects by diminishing the declination of the probability density function and the mean of a specific angular momentum, j_{θ}, as a measure of rotation. Another unique feature of the Langevin description is that rotation is maximized at a particular anisotropy while the stability of the rotation is minimized at a particular anisotropy or mass. Our results suggest that the Langevin dynamics description of the Brownian gyrator is intrinsically different from that with Brownian dynamics. In addition, j_{θ} is proven to be essential and convenient for estimating stochastic energetics such as heat currents and entropy production even in the underdamped regime.
Collapse
Affiliation(s)
- Youngkyoung Bae
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Sangyun Lee
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Juin Kim
- Department of Physics and Chemistry, Korea Air Force Academy, Cheongju, Chungbuk 28187, Korea
| | - Hawoong Jeong
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea.,Center for Complex systems, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| |
Collapse
|
9
|
Fazli Z, Naji A. Active particles with polar alignment in ring-shaped confinement. Phys Rev E 2021; 103:022601. [PMID: 33736018 DOI: 10.1103/physreve.103.022601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 01/13/2021] [Indexed: 12/17/2022]
Abstract
We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.
Collapse
Affiliation(s)
- Zahra Fazli
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.,School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| |
Collapse
|
10
|
GrandPre T, Klymko K, Mandadapu KK, Limmer DT. Entropy production fluctuations encode collective behavior in active matter. Phys Rev E 2021; 103:012613. [PMID: 33601608 DOI: 10.1103/physreve.103.012613] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 12/22/2020] [Indexed: 11/07/2022]
Abstract
We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particles. We also derive optimal control forces that realize the dynamics necessary to tune dissipation and manipulate the system between phases. In so doing, we uncover a general relationship between entropy production and pattern formation in active matter, as well as ways of controlling it.
Collapse
Affiliation(s)
- Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94609, USA
| | - Katherine Klymko
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94609, USA.,Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - David T Limmer
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Department of Chemistry, University of California, Berkeley, California 94609, USA.,Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Kavli Energy NanoScience Institute, Berkeley, California 94609, USA
| |
Collapse
|
11
|
Das A, Limmer DT. Variational design principles for nonequilibrium colloidal assembly. J Chem Phys 2021; 154:014107. [DOI: 10.1063/5.0038652] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Avishek Das
- Department of Chemistry, University of California, Berkeley, California 94609, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94609, USA
- Kavli Energy NanoScience Institute, Berkeley, California 94609, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| |
Collapse
|
12
|
Gutierrez-Martinez LL, Sandoval M. Inertial effects on trapped active matter. J Chem Phys 2020; 153:044906. [DOI: 10.1063/5.0011270] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico
| |
Collapse
|
13
|
Shabanniya MR, Naji A. Active dipolar spheroids in shear flow and transverse field: Population splitting, cross-stream migration, and orientational pinning. J Chem Phys 2020; 152:204903. [PMID: 32486664 DOI: 10.1063/5.0002757] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
We study the steady-state behavior of active, dipolar, Brownian spheroids in a planar channel subjected to an imposed Couette flow and an external transverse field, applied in the "downward" normal-to-flow direction. The field-induced torque on active spheroids (swimmers) is taken to be of magnetic form by assuming that they have a permanent magnetic dipole moment, pointing along their self-propulsion (swim) direction. Using a continuum approach, we show that a host of behaviors emerges over the parameter space spanned by the particle aspect ratio, self-propulsion and shear/field strengths, and the channel width. The cross-stream migration of the model swimmers is shown to involve a regime of linear response (quantified by a linear-response factor) in weak fields. For prolate swimmers, the weak-field behavior crosses over to a regime of full swimmer migration to the bottom half of the channel in strong fields. For oblate swimmers, a counterintuitive regime of reverse migration arises in intermediate fields, where a macroscopic fraction of swimmers reorient and swim to the top channel half at an acute "upward" angle relative to the field axis. The diverse behaviors reported here are analyzed based on the shear-induced population splitting (bimodality) of the swim orientation, giving two distinct, oppositely polarized, swimmer subpopulations (albeit very differently for prolate/oblate swimmers) in each channel half. In strong fields, swimmers of both types exhibit net upstream currents relative to the laboratory frame. The onsets of full migration and net upstream current depend on the aspect ratio, enabling efficient particle separation strategies in microfluidic setups.
Collapse
Affiliation(s)
- Mohammad Reza Shabanniya
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| |
Collapse
|
14
|
Vastola JJ, Holmes WR. Chemical Langevin equation: A path-integral view of Gillespie's derivation. Phys Rev E 2020; 101:032417. [PMID: 32289899 DOI: 10.1103/physreve.101.032417] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 02/25/2020] [Indexed: 12/16/2022]
Abstract
In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation (CME). In this work, we construct an original path-integral description of the CME and show how applying Gillespie's two conditions to it directly leads to a path-integral equivalent to the CLE. We compare this approach to the path-integral equivalent of a large system size derivation and show that they are qualitatively different. In particular, both approaches involve converting many sums into many integrals, and the difference between the two methods is essentially the difference between using the Euler-Maclaurin formula and using Riemann sums. Our results shed light on how path integrals can be used to conceptualize coarse-graining biochemical systems and are readily generalizable.
Collapse
Affiliation(s)
- John J Vastola
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee, USA and Quantitative Systems Biology Center, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - William R Holmes
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee, USA; Quantitative Systems Biology Center, Vanderbilt University, Nashville, Tennessee 37235, USA; and Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37235, USA
| |
Collapse
|
15
|
Dal Cengio S, Levis D, Pagonabarraga I. Linear Response Theory and Green-Kubo Relations for Active Matter. PHYSICAL REVIEW LETTERS 2019; 123:238003. [PMID: 31868450 DOI: 10.1103/physrevlett.123.238003] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Indexed: 05/12/2023]
Abstract
We address the question of how interacting active systems in a nonequilibrium steady state respond to an external perturbation. We establish an extended fluctuation-dissipation theorem for active Brownian particles (ABP), which highlights the role played by the local violation of detailed balance due to activity. By making use of a Markovian approximation we derive closed Green-Kubo expressions for the diffusivity and mobility of ABP and quantify the deviations from the Stokes-Einstein relation. We compute the linear response function to an external force using unperturbed simulations of ABP and compare the results with the analytical predictions of the transport coefficients. Our results show the importance of the interplay between activity and interactions in the departure from equilibrium linear response.
Collapse
Affiliation(s)
- Sara Dal Cengio
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E08028 Barcelona, Spain
| | - Demian Levis
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E08028 Barcelona, Spain
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
- UBICS University of Barcelona Institute of Complex Systems, Martí i Franquès 1, E08028 Barcelona, Spain
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E08028 Barcelona, Spain
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
- UBICS University of Barcelona Institute of Complex Systems, Martí i Franquès 1, E08028 Barcelona, Spain
| |
Collapse
|
16
|
|