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Ivchenko NA, Lebedev VV, Vergeles SS. Mixing in two-dimensional shear flow with smooth fluctuations. Phys Rev E 2024; 110:015102. [PMID: 39160955 DOI: 10.1103/physreve.110.015102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Accepted: 05/22/2024] [Indexed: 08/21/2024]
Abstract
Chaotic variations in flow speed up mixing of scalar fields via intensified stirring. This paper addresses the statistical properties of a passive scalar field mixing in a regular shear flow with random fluctuations against its background. We consider two-dimensional flow with shear component dominating over smooth fluctuations. Such flow is supposed to model passive scalar mixing, e.g., inside a large-scale coherent vortex forming in two-dimensional turbulence or in elastic turbulence in a microchannel. We examine both the decaying case and the case of the continuous forcing of the scalar variances. In both cases dynamics possesses strong intermittency, which can be characterized via the single-point moments and correlation functions calculated in our work. We present general qualitative properties of pair correlation function as well as certain quantitative results obtained in the framework of the model with fluctuations that are short correlated in time.
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Ornigotti L, Filip R. Stroboscopic thermally-driven mechanical motion. Sci Rep 2022; 12:20091. [PMID: 36418396 PMCID: PMC9684504 DOI: 10.1038/s41598-022-24074-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 11/09/2022] [Indexed: 11/25/2022] Open
Abstract
Unstable nonlinear systems can produce a large displacement driven by a small thermal initial noise. Such inherently nonlinear phenomena are stimulating in stochastic physics, thermodynamics, and in the future even in quantum physics. In one-dimensional mechanical instabilities, recently made available in optical levitation, the rapidly increasing noise accompanying the unstable motion reduces a displacement signal already in its detection. It limits the signal-to-noise ratio for upcoming experiments, thus constraining the observation of such essential nonlinear phenomena and their further exploitation. An extension to a two-dimensional unstable dynamics helps to separate the desired displacement from the noisy nonlinear driver to two independent variables. It overcomes the limitation upon observability, thus enabling further exploitation. However, the nonlinear driver remains unstable and rapidly gets noisy. It calls for a challenging high-order potential to confine the driver dynamics and rectify the noise. Instead, we propose and analyse a feasible stroboscopically-cooled driver that provides the desired detectable motion with sufficiently high signal-to-noise ratio. Fast and deep cooling, together with a rapid change of the driver stiffness, are required to reach it. However, they have recently become available in levitating optomechanics. Therefore, our analysis finally opens the road to experimental investigation of thermally-driven motion in nonlinear systems, its thermodynamical analysis, and future quantum extensions.
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Affiliation(s)
- Luca Ornigotti
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46, Olomouc, Czech Republic.
- Quantum Optics, Quantum Nanophysics and Quantum Information, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Wien, Austria.
| | - Radim Filip
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46, Olomouc, Czech Republic
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Ornigotti L, Filip R. Uncertainty-induced instantaneous speed and acceleration of a levitated particle. Sci Rep 2021; 11:18185. [PMID: 34521904 PMCID: PMC8440777 DOI: 10.1038/s41598-021-97663-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 08/23/2021] [Indexed: 11/17/2022] Open
Abstract
Levitating nanoparticles trapped in optical potentials at low pressure open the experimental investigation of nonlinear ballistic phenomena. With engineered non-linear potentials and fast optical detection, the observation of autonomous transient mechanical effects, such as instantaneous speed and acceleration stimulated purely by initial position uncertainty, are now achievable. By using parameters of current low pressure experiments, we simulate and analyse such uncertainty-induced particle ballistics in a cubic optical potential demonstrating their evolution, faster than their standard deviations, justifying the feasibility of the experimental verification. We predict, the maxima of instantaneous speed and acceleration distributions shift alongside the potential force, while the maximum of position distribution moves opposite to it. We report that cryogenic cooling is not necessary in order to observe the transient effects, while a low uncertainty in initial particle speed is required, via cooling or post-selection, to not mask the effects. These results stimulate the discussion for both attractive stochastic thermodynamics, and extension of recently explored quantum regime.
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Affiliation(s)
- Luca Ornigotti
- Department of Optics, Palacký University, 17. Listopadu 1192/12, 771 46, Olomouc, Czech Republic.
| | - Radim Filip
- Department of Optics, Palacký University, 17. Listopadu 1192/12, 771 46, Olomouc, Czech Republic
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Hastings A, Abbott KC, Cuddington K, Francis TB, Lai YC, Morozov A, Petrovskii S, Zeeman ML. Effects of stochasticity on the length and behaviour of ecological transients. J R Soc Interface 2021; 18:20210257. [PMID: 34229460 DOI: 10.1098/rsif.2021.0257] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system's transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.
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Affiliation(s)
- Alan Hastings
- Department of Environmental Science and Policy, University of California, Davis, CA 95616, USA.,Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
| | - Karen C Abbott
- Department of Biology, Case Western Reserve University, Cleveland, OH 44106, USA
| | - Kim Cuddington
- Department of Biology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Tessa B Francis
- Puget Sound Institute, University of Washington Tacoma, Tacoma, WA 98421, USA
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
| | - Andrew Morozov
- School of Mathematics and Actuarial Science, University of Leicester, Leicester LE1 7RH, UK.,Institute of Ecology and Evolution, Russian Academy of Sciences, Leninsky pr. 33, Moscow 117071, Russia
| | - Sergei Petrovskii
- School of Mathematics and Actuarial Science, University of Leicester, Leicester LE1 7RH, UK.,Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russia
| | - Mary Lou Zeeman
- Department of Mathematics, Bowdoin College, Brunswick, ME 04011, USA
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Capała K, Padash A, Chechkin AV, Shokri B, Metzler R, Dybiec B. Lévy noise-driven escape from arctangent potential wells. CHAOS (WOODBURY, N.Y.) 2020; 30:123103. [PMID: 33380056 DOI: 10.1063/5.0021795] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 11/04/2020] [Indexed: 06/12/2023]
Abstract
The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Lévy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Lévy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Lévy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.
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Affiliation(s)
- Karol Capała
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland
| | - Amin Padash
- Department of Physics, Shahid Beheshti University, 19839-69411 Tehran, Iran
| | - Aleksei V Chechkin
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Babak Shokri
- Department of Physics, Shahid Beheshti University, 19839-69411 Tehran, Iran
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Bartłomiej Dybiec
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland
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Dubkov AA, Dybiec B, Spagnolo B, Kharcheva A, Guarcello C, Valenti D. Statistics of residence time for Lévy flights in unstable parabolic potentials. Phys Rev E 2020; 102:042142. [PMID: 33212570 DOI: 10.1103/physreve.102.042142] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 09/22/2020] [Indexed: 11/07/2022]
Abstract
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
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Affiliation(s)
- Alexander A Dubkov
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia
| | - Bartłomiej Dybiec
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland
| | - Bernardo Spagnolo
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia.,Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123 Catania, Italy
| | - Anna Kharcheva
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia.,Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy
| | - Claudio Guarcello
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy.,INFN, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
| | - Davide Valenti
- Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,CNR-IRIB, Consiglio Nazionale delle Ricerche-Istituto per la Ricerca e l'Innovazione Biomedica, Via Ugo La Malfa 153, 90146 Palermo, Italy
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Falasco G, Esposito M. Dissipation-Time Uncertainty Relation. PHYSICAL REVIEW LETTERS 2020; 125:120604. [PMID: 33016734 DOI: 10.1103/physrevlett.125.120604] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2020] [Accepted: 08/14/2020] [Indexed: 05/10/2023]
Abstract
We show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff ⟨S[over ˙]_{e}⟩T≥k_{B} between the entropy flow ⟨S[over ˙]_{e}⟩ into the reservoirs and the mean time T to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.
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Affiliation(s)
- Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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Kolář M, Ryabov A, Filip R. Heat capacities of thermally manipulated mechanical oscillator at strong coupling. Sci Rep 2019; 9:10855. [PMID: 31350419 PMCID: PMC6659702 DOI: 10.1038/s41598-019-47288-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2018] [Accepted: 07/08/2019] [Indexed: 11/29/2022] Open
Abstract
Coherent quantum oscillators are basic physical systems both in quantum statistical physics and quantum thermodynamics. Their realizations in lab often involve solid-state devices sensitive to changes in ambient temperature. We represent states of the solid-state optomechanical oscillator with temperature-dependent frequency by equivalent states of the mechanical oscillator with temperature-dependent energy levels. We interpret the temperature dependence as a consequence of strong coupling between the oscillator and the heat bath. We explore parameter regimes corresponding to anomalous behavior of mechanical and thermodynamic characteristics as a consequence of the strong coupling: (i) The localization and the purification induced by heating, and (ii) the negativity of two generalized heat capacities. The capacities can be used to witness non-linearity in the temperature dependency of the energy levels. Our phenomenological experimentally-oriented approach can stimulate development of new optomechanical and thermomechanical experiments exploring basic concepts of strong coupling thermodynamics.
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Affiliation(s)
- Michal Kolář
- Palacký University, Department of Optics, 17. listopadu 1192/12, 771 46, Olomouc, Czech Republic.
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00, Praha, Czech Republic
- Centro de Física Teórica e Computacional, Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, P-1749-016, Lisboa, Portugal
| | - Radim Filip
- Palacký University, Department of Optics, 17. listopadu 1192/12, 771 46, Olomouc, Czech Republic
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Jinwoo L. Fluctuation Theorem of Information Exchange within an Ensemble of Paths Conditioned on Correlated-Microstates. ENTROPY 2019; 21:e21050477. [PMID: 33267191 PMCID: PMC7514966 DOI: 10.3390/e21050477] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Revised: 05/02/2019] [Accepted: 05/06/2019] [Indexed: 11/16/2022]
Abstract
Fluctuation theorems are a class of equalities that express universal properties of the probability distribution of a fluctuating path functional such as heat, work or entropy production over an ensemble of trajectories during a non-equilibrium process with a well-defined initial distribution. Jinwoo and Tanaka (Jinwoo, L.; Tanaka, H. Sci. Rep.2015, 5, 7832) have shown that work fluctuation theorems hold even within an ensemble of paths to each state, making it clear that entropy and free energy of each microstate encode heat and work, respectively, within the conditioned set. Here we show that information that is characterized by the point-wise mutual information for each correlated state between two subsystems in a heat bath encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange (Sagawa, T.; Ueda, M. Phys. Rev. Lett.2012, 109, 180602) by showing that the fluctuation theorem holds even within an ensemble of paths that reach a correlated state during dynamic co-evolution of two subsystems.
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Affiliation(s)
- Lee Jinwoo
- Department of Mathematics, Kwangwoon University, 20 Kwangwoon-ro, Seoul 01897, Korea
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