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Raja Venkatesh A, Le KH, Weld DM, Brandman O. Diffusive lensing as a mechanism of intracellular transport and compartmentalization. eLife 2024; 12:RP89794. [PMID: 38896469 PMCID: PMC11186627 DOI: 10.7554/elife.89794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/21/2024] Open
Abstract
While inhomogeneous diffusivity has been identified as a ubiquitous feature of the cellular interior, its implications for particle mobility and concentration at different length scales remain largely unexplored. In this work, we use agent-based simulations of diffusion to investigate how heterogeneous diffusivity affects the movement and concentration of diffusing particles. We propose that a nonequilibrium mode of membrane-less compartmentalization arising from the convergence of diffusive trajectories into low-diffusive sinks, which we call 'diffusive lensing,' is relevant for living systems. Our work highlights the phenomenon of diffusive lensing as a potentially key driver of mesoscale dynamics in the cytoplasm, with possible far-reaching implications for biochemical processes.
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Affiliation(s)
- Achuthan Raja Venkatesh
- Department of Biochemistry, Stanford UniversityStanfordUnited States
- Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) MohaliMohaliIndia
| | - Kathy H Le
- Department of Biochemistry, Stanford UniversityStanfordUnited States
| | - David M Weld
- Department of Physics, University of California, Santa BarbaraSanta BarbaraUnited States
| | - Onn Brandman
- Department of Biochemistry, Stanford UniversityStanfordUnited States
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2
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Dos Santos MAF, Menon L, Anteneodo C. Efficiency of random search with space-dependent diffusivity. Phys Rev E 2022; 106:044113. [PMID: 36397526 DOI: 10.1103/physreve.106.044113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
We address the problem of random search for a target in an environment with a space-dependent diffusion coefficient D(x). Considering a general form of the diffusion differential operator that includes Itô, Stratonovich, and Hänggi-Klimontovich interpretations of the associated stochastic process, we obtain and analyze the first-passage-time distribution and use it to compute the search efficiency E=〈1/t〉. For the paradigmatic power-law diffusion coefficient D(x)=D_{0}|x|^{α}, where x is the distance from the target and α<2, we show the impact of the different interpretations. For the Stratonovich framework, we obtain a closed-form expression for E, valid for arbitrary diffusion coefficient D(x). This result depends only on the distribution of diffusivity values and not on its spatial organization. Furthermore, the analytical expression predicts that a heterogeneous diffusivity profile leads to a lower efficiency than the homogeneous one with the same average level within the space between the target and the searcher initial position, but this efficiency can be exceeded for other interpretations.
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Affiliation(s)
- M A F Dos Santos
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900 Rio de Janeiro, Brazil
| | - L Menon
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900 Rio de Janeiro, Brazil
| | - C Anteneodo
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900 Rio de Janeiro, Brazil
- Institute of Science and Technology for Complex Systems, INCT-SC, Brazil
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3
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Belousov R, Hassanali A, Roldán É. Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics. Phys Rev E 2022; 106:014103. [PMID: 35974517 DOI: 10.1103/physreve.106.014103] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 05/20/2022] [Indexed: 06/15/2023]
Abstract
Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g., the diffusion coefficient or the heat conductivity, which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated because two alternative formulations of the inhomogeneous transport equations exist in the literature-the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Büttikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor, and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film.
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Affiliation(s)
- Roman Belousov
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Ali Hassanali
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Édgar Roldán
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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4
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Ignacio M, Bagheri M, Chubynsky MV, de Haan HW, Slater GW. Diffusivity interfaces in lattice Monte Carlo simulations: Modeling inhomogeneous delivery and release systems. Phys Rev E 2022; 105:064135. [PMID: 35854606 DOI: 10.1103/physreve.105.064135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 06/13/2022] [Indexed: 11/07/2022]
Abstract
Lattice Monte Carlo (LMC) simulations are widely used to investigate diffusion-controlled problems such as drug-release systems. The presence of an inhomogeneous diffusivity environment raises subtle questions about the interpretation of stochastic dynamics in the overdamped limit, an issue sometimes referred to as the "Ito-Stratonovich-isothermal dilemma." We propose a LMC formalism that includes the different stochastic interpretations in order to model the diffusion of particles in a space-dependent diffusivity landscape. Using as an example a simple inhomogeneous one-dimensional system with a diffusivity interface and different boundary conditions, we demonstrate that we can properly reproduce the steady state and dynamic properties of these systems and that these properties do depend on the choice of calculus. In particular, we argue that the version of the LMC algorithm that uses Ito calculus, which is commonly used to model drug delivery systems, should be replaced by the isothermal version for most applications. Our LMC methodology provides an efficient alternative to Langevin simulations for a wide class of space-dependent diffusion problems.
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Affiliation(s)
- M Ignacio
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - M Bagheri
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - M V Chubynsky
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - H W de Haan
- Department of Physics, Ontario Tech University, Oshawa, Ontario L1H 7K4, Canada
| | - G W Slater
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
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5
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Noise distorts the epigenetic landscape and shapes cell-fate decisions. Cell Syst 2021; 13:83-102.e6. [PMID: 34626539 DOI: 10.1016/j.cels.2021.09.002] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Revised: 06/21/2021] [Accepted: 09/02/2021] [Indexed: 12/24/2022]
Abstract
The Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent single-cell transcriptomic data provide new opportunities for quantifying this originally conceptual tool, offering insight into the gene regulatory networks underlying cellular development. While many methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use simple models to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data. A record of this paper's transparent peer review process is included in the supplemental information.
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Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems. ENTROPY 2021; 23:e23091125. [PMID: 34573750 PMCID: PMC8470578 DOI: 10.3390/e23091125] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Revised: 08/25/2021] [Accepted: 08/25/2021] [Indexed: 11/17/2022]
Abstract
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models-reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.
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Hashemi M, Vattikonda AN, Sip V, Guye M, Bartolomei F, Woodman MM, Jirsa VK. The Bayesian Virtual Epileptic Patient: A probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. Neuroimage 2020; 217:116839. [PMID: 32387625 DOI: 10.1016/j.neuroimage.2020.116839] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2019] [Revised: 04/02/2020] [Accepted: 04/07/2020] [Indexed: 12/28/2022] Open
Abstract
Despite the importance and frequent use of Bayesian frameworks in brain network modeling for parameter inference and model prediction, the advanced sampling algorithms implemented in probabilistic programming languages to overcome the inference difficulties have received relatively little attention in this context. In this technical note, we propose a probabilistic framework, namely the Bayesian Virtual Epileptic Patient (BVEP), which relies on the fusion of structural data of individuals to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. To invert the individualized whole-brain model employed in this study, we use the recently developed algorithms known as No-U-Turn Sampler (NUTS) as well as Automatic Differentiation Variational Inference (ADVI). Our results indicate that NUTS and ADVI accurately estimate the degree of epileptogenicity of brain regions, therefore, the hypothetical brain areas responsible for the seizure initiation and propagation, while the convergence diagnostics and posterior behavior analysis validate the reliability of the estimations. Moreover, we illustrate the efficiency of the transformed non-centered parameters in comparison to centered form of parameterization. The Bayesian framework used in this work proposes an appropriate patient-specific strategy for estimating the epileptogenicity of the brain regions to improve outcome after epilepsy surgery.
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Affiliation(s)
- M Hashemi
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France.
| | - A N Vattikonda
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France
| | - V Sip
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France
| | - M Guye
- Aix Marseille Univ, CNRS, CRMBM, Marseille, France
| | - F Bartolomei
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France; Epileptology Department, and Clinical Neurophysiology Department, Assistance Publique des Hôpitaux de Marseille, Marseille, France
| | - M M Woodman
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France
| | - V K Jirsa
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France.
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Piwowarczyk R, Selin M, Ihle T, Volpe G. Influence of sensorial delay on clustering and swarming. Phys Rev E 2019; 100:012607. [PMID: 31499896 DOI: 10.1103/physreve.100.012607] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Indexed: 06/10/2023]
Abstract
We show that sensorial delay alters the collective motion of self-propelling agents with aligning interactions: In a two-dimensional Vicsek model, short delays enhance the emergence of clusters and swarms, while long or negative delays prevent their formation. In order to quantify this phenomenon, we introduce a global clustering parameter based on the Voronoi tessellation, which permits us to efficiently measure the formation of clusters. Thanks to its simplicity, sensorial delay might already play a role in the organization of living organisms and can provide a powerful tool to engineer and dynamically tune the behavior of large ensembles of autonomous robots.
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Affiliation(s)
- Rafal Piwowarczyk
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
- Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
| | - Martin Selin
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
- Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
| | - Thomas Ihle
- Institute of Physics, University of Greifswald, DE-17489 Greifswald, Germany
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
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Maleki F, Becskei A. An open-loop approach to calculate noise-induced transitions. J Theor Biol 2017; 415:145-157. [PMID: 27993627 DOI: 10.1016/j.jtbi.2016.12.012] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2016] [Revised: 11/03/2016] [Accepted: 12/13/2016] [Indexed: 12/20/2022]
Abstract
Bistability permits the co-existence of two distinct cell fates in a population of genetically identical cells. Noise induced transitions between two fates of a bistable system are difficult to calculate due to the intricate interplay between nonlinear dynamics and noise in bistable positive feedback loops. Here we opened multivariable feedback loops at the slowest variable to obtain the open-loop function and the fluctuations in the open-loop output. By the subsequent reclosing of the loop, we calculated the mean first passage time (MFPT) using the Fokker-Planck equation in good agreement with the exact stochastic simulation. When an external component interacts with a feedback component, it amplifies the extrinsic noise in the loop. Consequently, the open-loop function is shifted and the transition rates between the two states in the closed loop are increased. Despite this shift, the open-loop output reflects the system faithfully to predict the MFPT in the feedback loop. Therefore, the open-loop approach can help theoretical analysis. Furthermore, the measurement of the mean value, variance, and the reaction time-scale of the open-loop output permits the prediction of MFPT simply from experimental data, which underscores the practical value of the stochastic open-loop approach.
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Affiliation(s)
- Farzaneh Maleki
- Biozentrum, Computational and systems biology, University of Basel, 4056 Basel, Switzerland
| | - Attila Becskei
- Biozentrum, Computational and systems biology, University of Basel, 4056 Basel, Switzerland.
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Kazakevičius R, Ruseckas J. Influence of external potentials on heterogeneous diffusion processes. Phys Rev E 2016; 94:032109. [PMID: 27739692 DOI: 10.1103/physreve.94.032109] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2016] [Indexed: 06/06/2023]
Abstract
In this paper we consider heterogeneous diffusion processes with the power-law dependence of the diffusion coefficient on the position and investigate the influence of external forces on the resulting anomalous diffusion. The heterogeneous diffusion processes can yield subdiffusion as well as superdiffusion, depending on the behavior of the diffusion coefficient. We assume that not only the diffusion coefficient but also the external force has a power-law dependence on the position. We obtain analytic expressions for the transition probability in two cases: when the power-law exponent in the external force is equal to 2η-1, where 2η is the power-law exponent in the dependence of the diffusion coefficient on the position, and when the external force has a linear dependence on the position. We found that the power-law exponent in the dependence of the mean square displacement on time does not depend on the external force; this force changes only the anomalous diffusion coefficient. In addition, the external force having the power-law exponent different from 2η-1 limits the time interval where the anomalous diffusion occurs. We expect that the results obtained in this paper may be relevant for a more complete understanding of anomalous diffusion processes.
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Affiliation(s)
- Rytis Kazakevičius
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10222 Vilnius, Lithuania
| | - Julius Ruseckas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10222 Vilnius, Lithuania
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11
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Sancho JM. Brownian colloids in underdamped and overdamped regimes with nonhomogeneous temperature. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062110. [PMID: 26764635 DOI: 10.1103/physreve.92.062110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2015] [Indexed: 06/05/2023]
Abstract
The motion of Brownian particles when temperature is spatially dependent is studied by stochastic simulations and theoretical analysis. Nonequilibrium steady probability distributions P(st)(z,v) for both underdamped and overdamped regimes are analyzed. The existence of local kinetic energy equipartition theorem is also discussed. The transition between both regimes is characterized by a dimensionless friction parameter. This study is applied to three physical systems of colloidal particles.
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Affiliation(s)
- J M Sancho
- Universitat de Barcelona, Departament d'Estructura i Constituents de la Matèria, Martí i Franqués, 1, 08028 Barcelona, Spain
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Tang Y, Yuan R, Chen J, Ao P. Controlling symmetry-breaking states by a hidden quantity in multiplicative noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052121. [PMID: 25493754 DOI: 10.1103/physreve.90.052121] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 06/04/2023]
Abstract
The inhomogeneity of multiplicative white noise leads to various coupling modes between deterministic and stochastic forces. We investigate the phase transition induced by the variation of the coupling mode through manipulating its characteristic parameter continuously. Even when the noise strength is fixed, an increase of this parameter can enhance or inhibit the symmetry-breaking state. We also propose a scheme to implement these phase transitions experimentally. Our result demonstrates that the coupling mode previously considered to be a mathematical convention serves as an additional quantity leading to physically observable phase transitions. This observation provides a mechanism to control the effect of noise without regulating the noise strength.
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Affiliation(s)
- Ying Tang
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ruoshi Yuan
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jianhong Chen
- ZhiYuan College, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ping Ao
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
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13
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Tang Y, Yuan R, Ao P. Nonequilibrium work relation beyond the Boltzmann-Gibbs distribution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062112. [PMID: 25019730 DOI: 10.1103/physreve.89.062112] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2014] [Indexed: 06/03/2023]
Abstract
The presence of multiplicative noise can alter measurements of forces acting on nanoscopic objects. Taking into account of multiplicative noise, we derive a series of nonequilibrium thermodynamical equalities as generalization of the Jarzynski equality, the detailed fluctuation theorem and the Hatano-Sasa relation. Our result demonstrates that the Jarzynski equality and the detailed fluctuation theorem remains valid only for systems with the Boltzmann-Gibbs distribution at the equilibrium state, but the Hatano-Sasa relation is robust with respect to different stochastic interpretations of multiplicative noise.
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Affiliation(s)
- Ying Tang
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ruoshi Yuan
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ping Ao
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
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