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Ali SY, Bauri P, Mondal D. Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance. J Phys Chem B 2024; 128:3824-3832. [PMID: 38616737 DOI: 10.1021/acs.jpcb.3c08066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/16/2024]
Abstract
We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.
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Affiliation(s)
- Syed Yunus Ali
- Department of Chemistry and Center for Atomic, Molecular, and Optical Sciences & Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
| | - Prashanta Bauri
- Department of Chemistry and Center for Atomic, Molecular, and Optical Sciences & Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
| | - Debasish Mondal
- Department of Chemistry and Center for Atomic, Molecular, and Optical Sciences & Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
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Modelling Asymmetric Unemployment Dynamics: The Logarithmic-Harmonic Potential Approach. ENTROPY 2022; 24:e24030400. [PMID: 35327911 PMCID: PMC8947050 DOI: 10.3390/e24030400] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Revised: 03/07/2022] [Accepted: 03/11/2022] [Indexed: 12/04/2022]
Abstract
Asymmetric behaviour has been documented in unemployment rates which increase quickly in recessions but decline relatively slowly during expansions. To model such asymmetric dynamics, this paper provides a rigorous derivation of the asymmetric mean-reverting fundamental dynamics governing the unemployment rate based on a model of a simple labour supply and demand (fundamental) relationship, and shows that the fundamental dynamics is a unique choice following the Rayleigh process. By analogy, such a fundamental can be considered as a one-dimensional overdamped Brownian particle moving in a logarithmic–harmonic potential well, and a simple prototype of stochastic heat engines. The solution of the model equation illustrates that the unemployment rate rises faster with more flattened potential well of the fundamental, more ample labour supply, and less anchored expectation of the unemployment rate, suggesting asymmetric unemployment rate dynamics in recessions and expansions. We perform explicit calibration of both the unemployment rate and fundamental dynamics, confirming the validity of our model for the fundamental dynamics.
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Chen H, Huang F. First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry. Phys Rev E 2022; 105:034109. [PMID: 35428076 DOI: 10.1103/physreve.105.034109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 02/18/2022] [Indexed: 06/14/2023]
Abstract
We investigate the first passage properties of a Brownian particle diffusing freely inside a d-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions of resetting rate γ and initial distance r of the particle to the center of the sphere. We find that when r>r_{c} there exists a nonzero optimal resetting rate γ_{opt} at which the MTA is a minimum, where r_{c}=sqrt[d/(d+4)]R and R is the radius of the sphere. As r increases, γ_{opt} exhibits a continuous transition from zero to nonzero at r=r_{c}. Furthermore, we consider that the particle lies between two two-dimensional or three-dimensional concentric spheres with absorbing boundaries, and obtain the domain in which resetting expedites the MTA, which is (R_{1},r_{c_{1}})∪(r_{c_{2}},R_{2}), with R_{1} and R_{2} being the radii of inner and outer spheres, respectively. Interestingly, when R_{1}/R_{2} is less than a critical value, γ_{opt} exhibits a discontinuous transition at r=r_{c_{1}}; otherwise, such a transition is continuous. However, at r=r_{c_{2}} the transition is always continuous.
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Affiliation(s)
- Hanshuang Chen
- School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, China
| | - Feng Huang
- Key Laboratory of Advanced Electronic Materials and Devices & School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
- Key Laboratory of Architectural Acoustic Environment of Anhui Higher Education Institutes, Hefei 230601, China
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Ali SY, Rafeek R, Mondal D. Geometric Brownian information engine: Upper bound of the achievable work under feedback control. J Chem Phys 2022; 156:014902. [PMID: 34998347 DOI: 10.1063/5.0069582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We design a geometric Brownian information engine by considering overdamped Brownian particles inside a two-dimensional monolobal confinement with irregular width along the transport direction. Under such detention, particles experience an effective entropic potential which has a logarithmic form. We employ a feedback control protocol as an outcome of error-free position measurement. The protocol comprises three stages: measurement, feedback, and relaxation. We reposition the center of the confinement to the measurement distance (xp) instantaneously when the position of the trapped particle crosses xp for the first time. Then, the particle is allowed for thermal relaxation. We calculate the extractable work, total information, and unavailable information associated with the feedback control using this equilibrium probability distribution function. We find the exact analytical value of the upper bound of extractable work as (53-2ln2)kBT. We introduce a constant force G downward to the transverse coordinate (y). A change in G alters the effective potential of the system and tunes the relative dominance of entropic and energetic contributions in it. The upper bound of the achievable work shows a crossover from (53-2ln2)kBT to 12kBT when the system changes from an entropy-dominated regime to an energy-dominated one. Compared to an energetic analog, the loss of information during the relaxation process is higher in the entropy-dominated region, which accredits the less value in achievable work. Theoretical predictions are in good agreement with the Langevin dynamics simulation studies.
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Affiliation(s)
- Syed Yunus Ali
- Department of Chemistry and Center for Molecular and Optical Sciences and Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
| | - Rafna Rafeek
- Department of Chemistry and Center for Molecular and Optical Sciences and Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
| | - Debasish Mondal
- Department of Chemistry and Center for Molecular and Optical Sciences and Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
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Ray S, Reuveni S. Resetting transition is governed by an interplay between thermal and potential energy. J Chem Phys 2021; 154:171103. [PMID: 34241053 DOI: 10.1063/5.0049642] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A dynamical process that takes a random time to complete, e.g., a chemical reaction, may either be accelerated or hindered due to resetting. Tuning system parameters, such as temperature, viscosity, or concentration, can invert the effect of resetting on the mean completion time of the process, which leads to a resetting transition. Although the resetting transition has been recently studied for diffusion in a handful of model potentials, it is yet unknown whether the results follow any universality in terms of well-defined physical parameters. To bridge this gap, we propose a general framework that reveals that the resetting transition is governed by an interplay between the thermal and potential energy. This result is illustrated for different classes of potentials that are used to model a wide variety of stochastic processes with numerous applications.
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Affiliation(s)
- Somrita Ray
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Shlomi Reuveni
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
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Wu LJ, Lee S, Park S, Eland LE, Wipat A, Holden S, Errington J. Geometric principles underlying the proliferation of a model cell system. Nat Commun 2020; 11:4149. [PMID: 32811832 PMCID: PMC7434903 DOI: 10.1038/s41467-020-17988-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 07/24/2020] [Indexed: 02/07/2023] Open
Abstract
Many bacteria can form wall-deficient variants, or L-forms, that divide by a simple mechanism that does not require the FtsZ-based cell division machinery. Here, we use microfluidic systems to probe the growth, chromosome cycle and division mechanism of Bacillus subtilis L-forms. We find that forcing cells into a narrow linear configuration greatly improves the efficiency of cell growth and chromosome segregation. This reinforces the view that L-form division is driven by an excess accumulation of surface area over volume. Cell geometry also plays a dominant role in controlling the relative positions and movement of segregating chromosomes. Furthermore, the presence of the nucleoid appears to influence division both via a cell volume effect and by nucleoid occlusion, even in the absence of FtsZ. Our results emphasise the importance of geometric effects for a range of crucial cell functions, and are of relevance for efforts to develop artificial or minimal cell systems.
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Affiliation(s)
- Ling Juan Wu
- Centre for Bacterial Cell Biology, Biosciences Institute, Medical School, Newcastle University, Richardson Road, Newcastle upon Tyne, NE2 4AX, UK.
| | - Seoungjun Lee
- grid.1006.70000 0001 0462 7212Centre for Bacterial Cell Biology, Biosciences Institute, Medical School, Newcastle University, Richardson Road, Newcastle upon Tyne, NE2 4AX UK ,grid.13097.3c0000 0001 2322 6764Present Address: Maurice Wohl Clinical Neuroscience Institute, Institute of Psychiatry, Psychology and Neuroscience, King’s College London, London, SE5 9RX UK
| | - Sungshic Park
- grid.1006.70000 0001 0462 7212Centre for Bacterial Cell Biology, Biosciences Institute, Medical School, Newcastle University, Richardson Road, Newcastle upon Tyne, NE2 4AX UK ,grid.1006.70000 0001 0462 7212Interdisciplinary Computing and Complex BioSystems research group, School of Computing, Newcastle University, Newcastle upon Tyne, NE4 5TG UK
| | - Lucy E. Eland
- grid.1006.70000 0001 0462 7212Centre for Bacterial Cell Biology, Biosciences Institute, Medical School, Newcastle University, Richardson Road, Newcastle upon Tyne, NE2 4AX UK ,grid.1006.70000 0001 0462 7212Interdisciplinary Computing and Complex BioSystems research group, School of Computing, Newcastle University, Newcastle upon Tyne, NE4 5TG UK
| | - Anil Wipat
- grid.1006.70000 0001 0462 7212Centre for Bacterial Cell Biology, Biosciences Institute, Medical School, Newcastle University, Richardson Road, Newcastle upon Tyne, NE2 4AX UK ,grid.1006.70000 0001 0462 7212Interdisciplinary Computing and Complex BioSystems research group, School of Computing, Newcastle University, Newcastle upon Tyne, NE4 5TG UK
| | - Séamus Holden
- grid.1006.70000 0001 0462 7212Centre for Bacterial Cell Biology, Biosciences Institute, Medical School, Newcastle University, Richardson Road, Newcastle upon Tyne, NE2 4AX UK
| | - Jeff Errington
- Centre for Bacterial Cell Biology, Biosciences Institute, Medical School, Newcastle University, Richardson Road, Newcastle upon Tyne, NE2 4AX, UK.
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Ray S, Reuveni S. Diffusion with resetting in a logarithmic potential. J Chem Phys 2020; 152:234110. [DOI: 10.1063/5.0010549] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Somrita Ray
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Shlomi Reuveni
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
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Das M, Ray DS. Landauer's blow-torch effect in systems with entropic potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052133. [PMID: 26651672 DOI: 10.1103/physreve.92.052133] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2015] [Indexed: 06/05/2023]
Abstract
We consider local heating of a part of a two-dimensional bilobal enclosure of a varying cross section confining a system of overdamped Brownian particles. Since varying cross section in higher dimension results in an entropic potential in lower dimension, local heating alters the relative stability of the entropic states. We show that this blow-torch effect modifies the entropic potential in a significant way so that the resultant effective entropic potential carries both the features of variation of width of the confinement and variation of temperature along the direction of transport. The reduced probability distribution along the direction of transport calculated by full numerical simulations in two dimensions agrees well with our analytical findings. The extent of population transfer in the steady state quantified in terms of the integrated probability of residence of the particles in either of the two lobes exhibits interesting variation with the mean position of the heated region. Our study reveals that heating around two particular zones of a given lobe maximizes population transfer to the other.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Das M. Capturing the Landauer bound through the application of a detailed Jarzynski equality for entropic memory erasure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062120. [PMID: 25615057 DOI: 10.1103/physreve.90.062120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2014] [Indexed: 06/04/2023]
Abstract
The states of an overdamped Brownian particle confined in a two-dimensional bilobal enclosure are considered to correspond to two binary values: 0 (left lobe) and 1 (right lobe). An ensemble of such particles represents bits of entropic information. An external bias is applied on the particles, equally distributed in two lobes, to drive them to a particular lobe erasing one kind of bit of information. It has been shown that the average work done for the entropic memory erasure process approaches the Landauer bound for a very slow erasure cycle. Furthermore, the detailed Jarzynski equality holds to a very good extent for the erasure protocol, so that the Landauer bound may be calculated irrespective of the time period of the erasure cycle in terms of the effective free-energy change for the process. The detailed Jarzynski equality applied to two subprocesses, namely the transition from entropic memory state 0 to state 1 and the transition from entropic memory state 1 to state 1, connects the work done on the system to the probability to occupy the two states under a time-reversed process. In the entire treatment, the work appears as a boundary effect of the physical confinement of the system not having a conventional potential energy barrier. Finally, an analytical derivation of the detailed and classical Jarzynski equality for Brownian movement in confined space with varying width has been proposed. Our analytical scheme supports the numerical simulations presented in this paper.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Ghosh PK. Communication: Escape kinetics of self-propelled Janus particles from a cavity: Numerical simulations. J Chem Phys 2014; 141:061102. [DOI: 10.1063/1.4892970] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Das M. Entropic memory erasure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032130. [PMID: 24730813 DOI: 10.1103/physreve.89.032130] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Indexed: 06/03/2023]
Abstract
We have considered a Brownian particle confined in a two-dimensional bilobal enclosure where the state of the particle represents a bit of information having binary value 0 (left lobe) or 1 (right lobe). A time linear force is applied on the particle, driving it selectively to a particular lobe, and thus erasing one bit of information. We explore the statistics of heat and work associated with memory erasure to realize the Landauer limit in the entropic domain. Our results suggest that the mean value of work done associated with the complete erasure procedure satisfies the Landauer bound even when the memory is purely entropic in nature.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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12
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Das M, Ray DS. Control of logic gates by dichotomous noise in energetic and entropic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032122. [PMID: 24125228 DOI: 10.1103/physreve.88.032122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2013] [Revised: 08/07/2013] [Indexed: 06/02/2023]
Abstract
We consider the stochastic response of a nonlinear dynamical system towards a combination of input signals. The response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier. We show how the input-output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time. This resonance manifests itself as a "logical" resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate. The role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two-state model using a master equation approach.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Das M, Mondal D, Ray DS. Logic gates for entropic transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041112. [PMID: 23214534 DOI: 10.1103/physreve.86.041112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2012] [Indexed: 06/01/2023]
Abstract
We consider a Brownian particle that is confined in a two-dimensional enclosure and driven by a combination of input signals. It has been shown that the logic gates can be formed by considering the state of the particle experiencing an entropic barrier as the output signal. For a consistent logical output, it is necessary to optimize the strength of the noise driving the particle for a given system size. The variation of the logical output behavior exhibits a turnover at an optimal value of system size parameter, implying a size resonance condition in entropic transport. The role of a transverse bias field used to tune the transport between the entropy dominated regime and the energy dominated regime is elucidated.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Das M, Mondal D, Ray DS. Shape fluctuation-induced dynamic hysteresis. J Chem Phys 2012; 136:114104. [DOI: 10.1063/1.3693333] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mondal D, Das M, Ray DS. Entropic dynamical hysteresis in a driven system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031128. [PMID: 22587059 DOI: 10.1103/physreve.85.031128] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2012] [Indexed: 05/31/2023]
Abstract
We show that the application of a time periodic field driving a Brownian particle between the two lobes of a two-dimensional bilobal enclosure results in a hysteresis loop in the variation of integrated probability of residence of the particle as a function of the field. The confinement of the particle is characterized by symmetry breaking of the hysteresis loop, and the area of the loop exhibits a turnover with variation of frequency of the field. This dynamical hysteresis is geometry controlled, entropic in nature, and amenable to theoretical analysis with a two-state model.
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Affiliation(s)
- Debasish Mondal
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
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Mondal D, Ray DS. Asymmetric stochastic localization in geometry controlled kinetics. J Chem Phys 2011; 135:194111. [DOI: 10.1063/1.3658486] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Debasish Mondal
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India.
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