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Debiossac M, Rosinberg ML, Lutz E, Kiesel N. Non-Markovian Feedback Control and Acausality: An Experimental Study. Phys Rev Lett 2022; 128:200601. [PMID: 35657900 DOI: 10.1103/physrevlett.128.200601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Revised: 01/31/2022] [Accepted: 04/01/2022] [Indexed: 06/15/2023]
Abstract
Causality is an important assumption underlying nonequilibrium generalizations of the second law of thermodynamics known as fluctuation relations. We here experimentally study the nonequilibrium statistical properties of the work and of the entropy production for an optically trapped, underdamped nanoparticle continuously subjected to a time-delayed feedback control. Whereas the non-Markovian feedback depends on the past position of the particle for a forward trajectory, it depends on its future position for a time-reversed path, and is therefore acausal. In the steady-state regime, we show that the corresponding fluctuation relations in the long-time limit exhibit a clear signature of this acausality, even though the time-reversed dynamics is not physically realizable.
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Affiliation(s)
- Maxime Debiossac
- University of Vienna, Faculty of Physics, VCQ, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Martin Luc Rosinberg
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Eric Lutz
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
| | - Nikolai Kiesel
- University of Vienna, Faculty of Physics, VCQ, Boltzmanngasse 5, A-1090 Vienna, Austria
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Lahiri S, Nghe P, Tans SJ, Rosinberg ML, Lacoste D. Information-theoretic analysis of the directional influence between cellular processes. PLoS One 2017; 12:e0187431. [PMID: 29121044 PMCID: PMC5679622 DOI: 10.1371/journal.pone.0187431] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2017] [Accepted: 10/19/2017] [Indexed: 11/25/2022] Open
Abstract
Inferring the directionality of interactions between cellular processes is a major challenge in systems biology. Time-lagged correlations allow to discriminate between alternative models, but they still rely on assumed underlying interactions. Here, we use the transfer entropy (TE), an information-theoretic quantity that quantifies the directional influence between fluctuating variables in a model-free way. We present a theoretical approach to compute the transfer entropy, even when the noise has an extrinsic component or in the presence of feedback. We re-analyze the experimental data from Kiviet et al. (2014) where fluctuations in gene expression of metabolic enzymes and growth rate have been measured in single cells of E. coli. We confirm the formerly detected modes between growth and gene expression, while prescribing more stringent conditions on the structure of noise sources. We furthermore point out practical requirements in terms of length of time series and sampling time which must be satisfied in order to infer optimally transfer entropy from times series of fluctuations.
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Affiliation(s)
- Sourabh Lahiri
- Gulliver laboratory, PSL Research University, ESPCI, 10 rue de Vauquelin, 75231 Paris Cedex 05, France
| | - Philippe Nghe
- Laboratory of Biochemistry, PSL Research University, ESPCI, 10 rue de Vauquelin, 75231 Paris Cedex 05, France
| | - Sander J. Tans
- FOM Institute AMOLF, Science Park, 104, 1098 XG Amsterdam, the Netherlands
| | - Martin Luc Rosinberg
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - David Lacoste
- Gulliver laboratory, PSL Research University, ESPCI, 10 rue de Vauquelin, 75231 Paris Cedex 05, France
- * E-mail:
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Rosinberg ML, Tarjus G, Munakata T. Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations. Phys Rev E 2017; 95:022123. [PMID: 28297974 DOI: 10.1103/physreve.95.022123] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2016] [Indexed: 11/07/2022]
Abstract
This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)PLEEE81539-375510.1103/PhysRevE.91.042114] was to derive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochastic fluctuations of time-integrated observables such as the heat exchanged with the environment, the extracted work, or the (apparent) entropy production. We use a path-integral formalism and focus on the long-time behavior in the stationary cooling regime, stressing the role of rare events. This is illustrated by a detailed analytical and numerical study of a Langevin harmonic oscillator driven by a linear feedback.
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Affiliation(s)
- M L Rosinberg
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - G Tarjus
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - T Munakata
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
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Rosinberg ML, Munakata T, Tarjus G. Stochastic thermodynamics of Langevin systems under time-delayed feedback control: Second-law-like inequalities. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:042114. [PMID: 25974446 DOI: 10.1103/physreve.91.042114] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2015] [Indexed: 06/04/2023]
Abstract
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.
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Affiliation(s)
- M L Rosinberg
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - T Munakata
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - G Tarjus
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France
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Munakata T, Rosinberg ML. Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control. Phys Rev Lett 2014; 112:180601. [PMID: 24856682 DOI: 10.1103/physrevlett.112.180601] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2014] [Indexed: 06/03/2023]
Abstract
Continuous feedback control of Langevin processes may be non-Markovian due to a time lag between the measurement and the control action. We show that this requires one to modify the basic relation between dissipation and time reversal and to include a contribution arising from the noncausal character of the reverse process. We then propose a new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state, which can also be regarded as the trajectory-dependent total entropy production. This leads to an extension of the second law, which takes a simple form in the long-time limit. As an illustration, we apply the general approach to linear systems that are both analytically tractable and experimentally relevant.
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Affiliation(s)
- T Munakata
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - M L Rosinberg
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Leoni F, Kierlik E, Rosinberg ML, Tarjus G. Spontaneous imbibition in disordered porous solids: a theoretical study of helium in silica aerogels. Langmuir 2011; 27:8160-8170. [PMID: 21657217 DOI: 10.1021/la201146h] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We present a theoretical study of spontaneous imbibition of liquid (4)He in silica aerogels focusing on the effect of porosity on the fluid dynamical behavior. We adopt a coarse-grained three-dimensional lattice-gas description like in previous studies of gas adsorption and capillary condensation and use a dynamical mean-field theory, assuming that capillary disorder predominates over permeability disorder as in recent phase-field models of spontaneous imbibition. Our results reveal a remarkable connection between imbibition and adsorption as also suggested by recent experiments. The imbibition front is always preceded by a precursor film, and the classical Lucas-Washburn √t scaling law is generally recovered, although some deviations may exist at large porosity. Moreover, the interface roughening is modified by wetting and confinement effects. Our results suggest that the interpretation of the recent experiments should be revised.
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Affiliation(s)
- F Leoni
- GIT-SPEC, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
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Kimizuka M, Munakata T, Rosinberg ML. Stochastic dynamics of N bistable elements with global time-delayed interactions: towards an exact solution of the master equations for finite N. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 82:041129. [PMID: 21230260 DOI: 10.1103/physreve.82.041129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2010] [Indexed: 05/30/2023]
Abstract
We consider a network of N noisy bistable elements with global time-delayed couplings. In a two-state description, where elements are represented by Ising spins, the collective dynamics is described by an infinite hierarchy of coupled master equations which was solved at the mean-field level in the thermodynamic limit. When the number of elements is finite, as is the case in actual laser networks, an analytical description was deemed so far intractable and numerical studies seemed to be necessary. In this paper we consider the case of two interacting elements and show that a partial analytical description of the stationary state is possible if the stochastic process is time symmetric. This requires some relationship between the transition rates to be satisfied.
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Affiliation(s)
- M Kimizuka
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
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Detcheverry F, Kierlik E, Rosinberg ML, Tarjus G. Gas adsorption and desorption in silica aerogels: a theoretical study of scattering properties. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:041511. [PMID: 16711813 DOI: 10.1103/physreve.73.041511] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Indexed: 05/09/2023]
Abstract
We present a numerical study of the structural correlations associated with gas adsorption and desorption in silica aerogels in order to provide a theoretical interpretation of scattering experiments. Following our earlier work, we use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis. We focus on the differences between the adsorption and desorption mechanisms and their signature in the fluid-fluid and gel-fluid structure factors as a function of temperature. At low temperature, but still in the regime where the isotherms are continuous, we find that the adsorbed fluid density, during both filling and draining, is correlated over distances that may be much larger than the gel correlation length. In particular, extended fractal correlations may occur during desorption, indicating the existence of a ramified cluster of vapor filled cavities. This also induces an important increase of the scattering intensity at small wave vectors. The similarity and differences with the scattering of fluids in other porous solids such as Vycor are discussed.
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Affiliation(s)
- F Detcheverry
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Detcheverry F, Kierlik E, Rosinberg ML, Tarjus G. Helium condensation in aerogel: avalanches and disorder-induced phase transition. Phys Rev E Stat Nonlin Soft Matter Phys 2005; 72:051506. [PMID: 16383610 DOI: 10.1103/physreve.72.051506] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2005] [Indexed: 05/05/2023]
Abstract
We present a detailed numerical study of the elementary condensation events (avalanches) associated to the adsorption of in silica aerogels. We use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis, neglecting thermal fluctuations and activated processes. We investigate the statistical properties of the avalanches, such as their number, size and shape along the adsorption isotherms as a function of gel porosity, temperature, and chemical potential. Our calculations predict the existence of a line of critical points in the temperature-porosity diagram where the avalanche size distribution displays a power-law behavior and the adsorption isotherms have a universal scaling form. The estimated critical exponents seem compatible with those of the field-driven random field Ising model at zero temperature.
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Affiliation(s)
- F Detcheverry
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
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Detcheverry F, Kierlik E, Rosinberg ML, Tarjus G. Mechanisms for gas adsorption and desorption in silica aerogels: the effect of temperature. Langmuir 2004; 20:8006-8014. [PMID: 15350065 DOI: 10.1021/la0488506] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We present a theoretical study of the adsorption and desorption mechanisms of fluids in silica aerogels, focusing on the effect of temperature. We adopt a coarse-grained lattice description in which the gel structure is generated by a diffusion-limited cluster-cluster aggregation algorithm and the fluid configurations are computed using local mean-field (i.e., density functional) theory. Our calculations reproduce qualitatively the changes in the shape of the hysteresis loops observed with (4)He in gels of varying porosity. We study in detail the morphology of the condensation and evaporation events that correspond to the irreversible processes (avalanches) which are at the origin of the hysteresis. Depending on porosity and temperature, these avalanches may be localized, involve regions that extend beyond the gel correlation length, or even span the entire sample. This makes difficult the characterization of aerogels based on analyzing sorption isotherms.
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Affiliation(s)
- F Detcheverry
- Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
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Detcheverry F, Kierlik E, Rosinberg ML, Tarjus G. Local mean-field study of capillary condensation in silica aerogels. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 68:061504. [PMID: 14754209 DOI: 10.1103/physreve.68.061504] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2003] [Indexed: 05/24/2023]
Abstract
We apply local mean-field (i.e., density functional) theory to a lattice model of a fluid in contact with a dilute, disordered gel network. The gel structure is described by a diffusion-limited cluster aggregation model. We focus on the influence of porosity on both the hysteretic and the equilibrium behavior of the fluid as one varies the chemical potential at low temperature. We show that the shape of the hysteresis loop changes from smooth to rectangular as the porosity increases and that this change is associated with disorder-induced out-of-equilibrium phase transitions that differ in adsorption and in desorption. Our results provide insight in the behavior of 4He in silica aerogels.
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Affiliation(s)
- F Detcheverry
- Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
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Kierlik E, Monson PA, Rosinberg ML, Sarkisov L, Tarjus G. Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior. Phys Rev Lett 2001; 87:055701. [PMID: 11497783 DOI: 10.1103/physrevlett.87.055701] [Citation(s) in RCA: 109] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2000] [Indexed: 05/23/2023]
Abstract
We study the interplay between hysteresis and equilibrium behavior in capillary condensation of fluids in mesoporous disordered materials via a mean-field density functional theory of a disordered lattice-gas model. The approach reproduces all major features observed experimentally. We show that the simple van der Waals picture of metastability fails due to the appearance of a complex free-energy landscape with a large number of metastable states. In particular, hysteresis can occur both with and without an underlying equilibrium transition, and thermodynamic consistency is not satisfied along the hysteresis loop.
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Affiliation(s)
- E Kierlik
- Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Grollau S, Kierlik E, Rosinberg ML, Tarjus G. Thermodynamically self-consistent theory for the Blume-Capel model. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 63:041111. [PMID: 11308823 DOI: 10.1103/physreve.63.041111] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2000] [Indexed: 05/23/2023]
Abstract
We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.
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Affiliation(s)
- S Grollau
- Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Pitard E, Rosinberg ML, Stell G, Tarjus G. Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach. Phys Rev Lett 1995; 74:4361-4364. [PMID: 10058487 DOI: 10.1103/physrevlett.74.4361] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Dong W, Kierlik E, Rosinberg ML. Integral equations for a fluid near a random substrate. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1994; 50:4750-4753. [PMID: 9962554 DOI: 10.1103/physreve.50.4750] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Phan S, Kierlik E, Rosinberg ML, Bildstein B, Kahl G. Equivalence of two free-energy models for the inhomogeneous hard-sphere fluid. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993; 48:618-620. [PMID: 9960629 DOI: 10.1103/physreve.48.618] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kierlik E, Rosinberg ML. Density-functional theory for inhomogeneous fluids: Adsorption of binary mixtures. Phys Rev A 1991; 44:5025-5037. [PMID: 9906554 DOI: 10.1103/physreva.44.5025] [Citation(s) in RCA: 153] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kierlik E, Rosinberg ML. Free-energy density functional for the inhomogeneous hard-sphere fluid: Application to interfacial adsorption. Phys Rev A 1990; 42:3382-3387. [PMID: 9904418 DOI: 10.1103/physreva.42.3382] [Citation(s) in RCA: 202] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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