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Kumar V, Pal A, Shpielberg O. Emerging universality classes in thermally assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach. J Chem Phys 2024; 160:134107. [PMID: 38563303 DOI: 10.1063/5.0195570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Accepted: 03/01/2024] [Indexed: 04/04/2024] Open
Abstract
Thermal activation of a particle from a deep potential trap follows the Arrhenius law. Recently, this result has been generalized for interacting diffusive particles in the trap, revealing two universality classes-the Arrhenius class and the excluded volume class. The result was demonstrated with the aid of numerical analysis. Here, we present a perturbative hydrodynamic approach to analytically validate the existence and range of validity for the two universality classes.
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Affiliation(s)
- Vishwajeet Kumar
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Ohad Shpielberg
- Department of Mathematics and Physics, University of Haifa at Oranim, Kiryat Tivon 3600600, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Abba Khoushy Ave. 199, Haifa 3498838, Israel
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Kumar V, Pal A, Shpielberg O. Arrhenius law for interacting diffusive systems. Phys Rev E 2024; 109:L032101. [PMID: 38632768 DOI: 10.1103/physreve.109.l032101] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 02/08/2024] [Indexed: 04/19/2024]
Abstract
Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory-a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.
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Affiliation(s)
- Vishwajeet Kumar
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Ohad Shpielberg
- Department of Mathematics and Physics, University of Haifa at Oranim, Kiryat Tivon 3600600, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Abba Khoushy Avenue 199, Haifa 3498838, Israel
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Hartmann AK, Krajenbrink A, Le Doussal P. Probing the large deviations for the beta random walk in random medium. Phys Rev E 2024; 109:024122. [PMID: 38491613 DOI: 10.1103/physreve.109.024122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Accepted: 01/11/2024] [Indexed: 03/18/2024]
Abstract
We consider a discrete-time random walk on a one-dimensional lattice with space- and time-dependent random jump probabilities, known as the beta random walk. We are interested in the probability that, for a given realization of the jump probabilities (a sample), a walker starting at the origin at time t=0 is at position beyond ξsqrt[T/2] at time T. This probability fluctuates from sample to sample and we study the large-deviation rate function, which characterizes the tails of its distribution at large time T≫1. It is argued that, up to a simple rescaling, this rate function is identical to the one recently obtained exactly by two of the authors for the continuum version of the model. That continuum model also appears in the macroscopic fluctuation theory of a class of lattice gases, e.g., in the so-called KMP model of heat transfer. An extensive numerical simulation of the beta random walk, based on an importance sampling algorithm, is found in good agreement with the detailed analytical predictions. A first-order transition in the tilted measure, predicted to occur in the continuum model, is also observed in the numerics.
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Affiliation(s)
| | - Alexandre Krajenbrink
- Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, United Kingdom
- Le Lab Quantique, 58 rue d'Hauteville, 75010, Paris, France
| | - Pierre Le Doussal
- Laboratoire de Physique de l'École Normale Supérieure, PSL University, CNRS, Sorbonne Universités, 24 rue Lhomond, 75231 Paris, France
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Krajenbrink A, Le Doussal P. Crossover from the macroscopic fluctuation theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion. Phys Rev E 2023; 107:014137. [PMID: 36797871 DOI: 10.1103/physreve.107.014137] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 12/21/2022] [Indexed: 01/30/2023]
Abstract
We study the crossover from the macroscopic fluctuation theory (MFT), which describes one-dimensional stochastic diffusive systems at late times, to the weak noise theory (WNT), which describes the Kardar-Parisi-Zhang (KPZ) equation at early times. We focus on the example of the diffusion in a time-dependent random field, observed in an atypical direction which induces an asymmetry. The crossover is described by a nonlinear system which interpolates between the derivative and the standard nonlinear Schrodinger equations in imaginary time. We solve this system using the inverse scattering method for mixed-time boundary conditions introduced by us to solve the WNT. We obtain the rate function which describes the large deviations of the sample-to-sample fluctuations of the cumulative distribution of the tracer position. It exhibits a crossover as the asymmetry is varied, recovering both MFT and KPZ limits. We sketch how it is consistent with extracting the asymptotics of a Fredholm determinant formula, recently derived for sticky Brownian motions. The crossover mechanism studied here should generalize to a larger class of models described by the MFT. Our results apply to study extremal diffusion beyond Einstein's theory.
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Affiliation(s)
| | - Pierre Le Doussal
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France
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Bettelheim E, Smith NR, Meerson B. Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model. PHYSICAL REVIEW LETTERS 2022; 128:130602. [PMID: 35426706 DOI: 10.1103/physrevlett.128.130602] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Revised: 02/01/2022] [Accepted: 03/08/2022] [Indexed: 06/14/2023]
Abstract
We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability of the underlying equations of the macroscopic fluctuation theory. These equations are closely related to the derivative nonlinear Schrödinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978)JMAPAQ0022-248810.1063/1.523737 for the DNLS. We obtain explicit results for the exact large deviation function of the transferred heat for an initially localized heat pulse, where we uncover a nontrivial symmetry relation.
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Affiliation(s)
- Eldad Bettelheim
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Naftali R Smith
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer, 8499000, Israel
| | - Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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Shpielberg O, Pal A. Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies. Phys Rev E 2021; 104:064141. [PMID: 35030838 DOI: 10.1103/physreve.104.064141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 12/02/2021] [Indexed: 06/14/2023]
Abstract
A universal large N theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse-grained thermodynamic uncertainty relations-one of them being an activity bound. Importantly, the activity serves as a tighter bound for the entropy production in 1D systems. These results are particularly useful in the many-body regime, where typically a coarse-grained approach is required to handle the large microscopic state space.
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Affiliation(s)
- Ohad Shpielberg
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Mt. Carmel, Haifa 31905, Israel
| | - Arnab Pal
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University & Department of Physics, Indian Institute of Technology, Kanpur, Kanpur 208016, India
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Katira S, Garrahan JP, Mandadapu KK. Solvation in Space-time: Pretransition Effects in Trajectory Space. PHYSICAL REVIEW LETTERS 2018; 120:260602. [PMID: 30004722 DOI: 10.1103/physrevlett.120.260602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2017] [Revised: 03/01/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate pretransition effects in space-time in trajectories of systems in which the dynamics displays a first-order phase transition between distinct dynamical phases. These effects are analogous to those observed for thermodynamic first-order phase transitions, most notably the hydrophobic effect in water. Considering the (infinite temperature) East model as an elementary example, we study the properties of "space-time solvation" by examining trajectories where finite space-time regions are conditioned to be inactive in an otherwise active phase. We find that solvating an inactive region of space-time within an active trajectory shows two regimes in the dynamical equivalent of solvation free energy: an "entropic" small solute regime in which uncorrelated fluctuations are sufficient to evacuate activity from the solute, and an "energetic" large solute regime which involves the formation of a solute-induced inactive domain with an associated active-inactive interface bearing a dynamical interfacial tension. We also show that as a result of this dynamical interfacial tension there is a dynamical analog of the hydrophobic collapse that drives the assembly of large hydrophobes in water. We discuss the general relevance of these results to the properties of dynamical fluctuations in systems with slow collective relaxation such as glass formers.
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Affiliation(s)
- Shachi Katira
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Shpielberg O. Geometrical interpretation of dynamical phase transitions in boundary-driven systems. Phys Rev E 2017; 96:062108. [PMID: 29347441 DOI: 10.1103/physreve.96.062108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Indexed: 06/07/2023]
Abstract
Dynamical phase transitions are defined as nonanalytic points of the large deviation function of current fluctuations. We show that for boundary-driven systems, many dynamical phase transitions can be identified using the geometrical structure of an effective potential of a Hamiltonian, recovered from the macroscopic fluctuation theory description. Using this method we identify new dynamical phase transitions that could not be recovered using existing perturbative methods. Moreover, using the Hamiltonian picture, an experimental scheme is suggested to demonstrate an analog of dynamical phase transitions in linear, rather than exponential, time.
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Affiliation(s)
- Ohad Shpielberg
- Laboratoire de Physique Théorique de l'École Normale Supérieure de Paris, CNRS, ENS & PSL Research University, UPMC & Sorbonne Universités, 75005 Paris, France
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