Resolving coupled transport in space and time from molecular fluctuations in confined fluids

Ian C. Bourg; Th\^e Hoang Ngoc Minh

REVIEW 3 major objections 5 minor 49 references

Resolving coupled transport in space and time from molecular fluctuations in confined fluids

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Coupled transport in nanoconfined fluids is a space-time-resolved Onsager response kernel extracted from equilibrium molecular fluctuations, with momentum long-lived and nonlocal, charge fast and local, and the two linked through distinct…

desk verdict Textbook Kubo theory, but the first full 4x4 space-time response matrix for a confined charged fluid — worth refereeing, with a thermostat control and error bars required. read the letter →

arxiv 2608.04920 v1 pith:OVO24OCN submitted 2026-08-05 cond-mat.stat-mech cond-mat.mes-hallphysics.comp-phphysics.flu-dyn

Thê Hoang Ngoc Minh , Ian C. Bourg This is my paper · ORCID

classification cond-mat.stat-mechcond-mat.mes-hallphysics.comp-phphysics.flu-dyn PACS 05.60.-k47.61.-k

keywords nanoconfinedfluidsOnsagerresponsematrixspace-timekernelsmoleculardynamicselectrokineticcouplingGreen-Kuborelationsnonlocaltransportelectricaldoublelayer

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Nanoconfined flow, solute, heat, and charge transport are usually compressed into bulk coefficients and effective interfacial parameters such as slip lengths, zeta potentials, and resistances. The paper argues this compression discards the essential physics: under nanoconfinement the response of a fluid is spatially heterogeneous and has memory, so the right object is a space–time-resolved Onsager response matrix $R_{ab}(\mathbf r,\mathbf r',t)$ extracted from equilibrium current correlations. Using molecular dynamics of a charged Lennard–Jones fluid in a slit pore, it shows that momentum transport is a long-lived, nonlocal hydrodynamic mode across the pore, charge transport relaxes rapidly through localized ionic friction, and the off-diagonal electrokinetic kernels connect these two behaviors. If correct, every familiar transport coefficient is a fully integrated limit of this kernel, and nonlocal, history-dependent constitutive laws become the natural description at the nanoscale. The payoff would be a direct microscopic route to effective interfacial parameters and a new target for coarse-grained and data-driven transport models.

What carries the argument

The central object is the space–time-resolved Onsager response kernel $R_{ab}(\mathbf r,\mathbf r',t)$, the equilibrium correlation of local flux densities divided by $k_B T$, defined through Eq. (4). It carries the argument because all familiar transport quantities are projections of it: local–global kernels $K_{ab}(\mathbf z,t)$, stationary profiles $M_{ab}(\mathbf z)$, two-point responses $G_{ab}(\mathbf z,\mathbf z')$ (via Einstein–Helfand), global correlations $C_{ab}(t)$, and the Onsager matrix $L_{ab}$ as the full large-time integral. The paper deliberately stops before coarse graining and treats these correlations as the central observables, using the unsteady Stokes Green function only as a reference to interpret the hydrodynamic sector.

What would settle it

Run the same confined system under a weak, localized, time-dependent force (for instance a moving barrier or a small oscillating electric field localized near one wall) and compare the resulting flux at position z and time t with the convolution of the equilibrium kernel against the driving gradient; if the long-time tail predicted by the kernel does not match the nonequilibrium measurement, the identification of correlations with response fails. A simpler check is to re-extract $K_{nn}(z,t)$ in the microcanonical ensemble: the claimed long-lived hydrodynamic mode should persist without any thermostat.

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Extended reading notes

Core claim

The central claim, stated on its own terms, is that coupled transport in a nanoconfined fluid is fully described by the equilibrium correlation kernel $R_{ab}(\mathbf r,\mathbf r',t) = (k_B T)^{-1}\langle \mathbf j_a(\mathbf r,t)\,\mathbf j_b^\dagger(\mathbf r',0)\rangle_{\rm eq}$, and that this kernel, rather than its space/time integrals, is the physically meaningful response function under confinement. The paper shows in a charged Lennard-Jones slit that particle ($n$), solute ($s$), heat ($h$), and charge ($c$) channels organize in a block structure: $n$, $s$, and $h$ share long-lived, pore-spanning hydrodynamic relaxation while $c$ relaxes fast and locally; the reciprocal electro-osmotic and streaming-current kernels have the same integrated Onsager coefficient but distinct spatial and temporal pathways, with a backflow-like negative region in the electro-osmotic profile. Because the kernel is the pre-integrated object, Onsager reciprocity holds nonlocally, $\mathbf G_{ab}(\mathbf z,\mathbf z') = \mathbf G_{ba}(\mathbf z',\mathbf z)$, while one-sided projections need not be symmetric. Conventional coefficients, including the full Onsager matrix, are recovered by the successive integrations of Eq. (3), and effective parameters such as slip length or zeta potential are reinterpreted as coarse-grained summaries of this underlying field-level response.

Load-bearing premise

The whole derivation assumes the equilibrium current correlations measured in the thermostatted simulations are the true response kernels, which requires that the Nosé–Hoover damping does not alter the long-time dynamics behind the claimed hydrodynamic mode and that the chosen Irving–Kirkwood definitions, especially for the heat current, capture the physically relevant fluxes.

Editorial extensions

If this is right

Conventional transport coefficients follow as fully integrated limits of the response kernels: the Onsager matrix $L_{ab}$, conductivity, permeability, and mobility profiles all emerge from successive spatial and temporal integration.
Nanoscale momentum transport is genuinely nonlocal and long-lived (hydrodynamic modes crossing the pore), so single-point local closures and steady-state effective parameters miss the physics that matters.
Charge transport is fast, localized ionic friction; its stationary profile is near-bulk in the pore center, so charge relaxation can be modeled locally once the interfacial structure is retained.
Electrokinetic coupling is interfacial but nonlocal: EOF and streaming current have different dynamical pathways, and the sign of the integrated electrokinetic response depends on EDL spatial organization and hydrodynamic weighting, not just net charge.
Reciprocity lives at the kernel level; projected one-sided quantities need not be symmetric, giving a microscopic basis for nonlocal, history-dependent transport laws.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An extension the authors only gesture at: because Eq. (4) is a field-level Green–Kubo relation, the same protocol can yield frequency- and wavevector-dependent transport functions, turning the kernel into a microscopic impedance or memory function for nanofluidic devices.
The fitted unsteady-Stokes comparison suggests a testable prediction: the effective kinematic viscosity and confinement extracted from the time-dependent kernel should coincide with values from independent nonequilibrium or microcanonical measurements; disagreement would pinpoint thermostat artifacts.
The formalism implies that apparent violations of Onsager symmetry in projected or coarse-grained coefficients are projection artifacts; a direct check would be to construct coarse-grained coefficients from one-sided projections and verify that the full kernel still satisfies $G_{ab}(\mathbf z,\mathbf z')=G_{ba}(\mathbf z',\mathbf z)$.
A concrete extension to real materials would replace the minimal Lennard-Jones electrolyte with water-like models and check whether rotational and hydration modes add spectrally separated features to the heat and charge kernels, as the authors themselves note.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The thing to know: this paper takes a textbook result—the Kubo relation between equilibrium current correlations and response functions—and actually carries it out in field-resolved form for a confined charged fluid. That sounds incremental, but the resulting object, the full 4x4 space-time response kernel, is not something I've seen before, and the physical contrast between the long-lived nonlocal momentum channel and the short-lived localized charge channel is a clean, useful demonstration. The paper is honest and careful; the limitations section is unusually candid.

What's genuinely good: the derivation is clean, the MD implementation is described in detail (256 replicas, nonuniform bins, Irving-Kirkwood currents), and the excess-flux transformation in the SI shows they understand the representation-dependence of their object. The fact that the kernels are direct equilibrium correlations, not fitted to the hydrodynamic model, deals with the circularity concern—the Stokes fit is only an interpretive overlay.

Soft spots, in order of seriousness. First, the Nosé–Hoover thermostat with damping 0.1 is aggressive, and the paper's central claim about a long-lived hydrodynamic mode rests on correlation tails out to t > 1000. A thermostat that strongly couples to the fluid can renormalize or suppress those tails, and the paper gives no test of thermostat dependence. This is a real gap, not a nitpick. It doesn't sink the paper—the charge-localization result is less sensitive to this—but it means the headline 'hydrodynamic mode' needs a control. Second, the off-diagonal charge channel has enormous error bars (Table S2: L_cn/V = -1.8e-2 ± 2.8e-2), and Fig. 3 is shown without error bars. That's a presentation issue as much as a statistical one. Third, the heat current is convention-dependent; they acknowledge it, but it limits the quantitative force of the heat sector. Finally, data and code are promised but not yet public; for a paper this simulation-heavy, that should be a condition of acceptance.

The thermodynamic interpretation (the backflow asymmetry between EOF and SC) is suggestive but not fully nailed down; I'd trust the kernels more than the narrative.

Who is this for? Nanofluidics and MD practitioners who want a more complete microscopic description than integrated Onsager coefficients. It's a proof of principle, not a breakthrough, but it's a useful one.

My recommendation: send it out for peer review, but require the thermostat test and error bars on the full matrix before acceptance. The framework deserves to be evaluated by the community.

Best.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a space–time-resolved generalization of the Onsager response matrix for confined fluids, in which transport is described by kernels R_ab(r,r',t) extracted from equilibrium current correlations via Eq. (4). The authors simulate a charged Lennard-Jones fluid in a slit pore, compute local–global and local–local response projections, and report a striking separation: the particle channel exhibits a long-lived, nonlocal momentum response that they identify with unsteady Stokes hydrodynamics, while the charge channel relaxes rapidly and locally. Off-diagonal particle–charge kernels are used to examine electro-osmotic flow and streaming current pathways, and a full 4×4 matrix for particle, solute, heat, and charge transport is presented, together with an excess-flux transformation in the Supplementary Material. The SI contains the linear-response derivation, detailed simulation parameters, uncertainty statements, analytical reference models, and a candid Limitations section.

Significance. If the central results are reliable, the framework is a valuable step beyond the usual reduction of nanoscale transport to effective coefficients: it makes the full spatiotemporal structure of coupled transport accessible from equilibrium MD and clarifies where Onsager reciprocity lives after coarse-graining. The paper is commendably explicit in deriving Eq. (4) from Liouville dynamics, in describing the 256-replica sampling protocol, in separating measured kernels from fitted reference models, and in acknowledging representation dependence and statistical cost. The commitment to public deposition of simulation data and analysis scripts, if honored, is an additional strength. The significance is currently tempered by two load-bearing concerns: the possible distortion of long-time correlations by the Nosé–Hoover thermostat, and the large statistical uncertainty in the off-diagonal charge sector that nonetheless carries several of the paper's interpretive claims.

major comments (3)

[SI Materials and Methods, MD simulations; SI Eqs. (S34)–(S41)] The identification of measured correlations with response kernels in Eq. (4) is derived under Hamiltonian dynamics (SI Eqs. (S34)–(S41)), but the production runs use a Nosé–Hoover thermostat with damping time 0.1, which can couple to molecular and possibly hydrodynamic time scales. The paper provides no test of thermostat dependence, so the 'long-lived hydrodynamic mode' that anchors the main claim could be an artifact of the thermostat rather than intrinsic confined-fluid memory. Please add an NVE comparison or a thermostat-damping variation (for example, damping times from 0.1 to 10) and show that the slow kernels and the integrated L_nn(t) are unchanged within uncertainty.
[Table S2; Figs. 2 and 3] The off-diagonal charge entries in Table S2 are statistically indistinguishable from zero: L_cn/V = (-1.8 ± 2.8)×10^-2 and L_ch/V = (-2.3 ± 2.6)×10^-1. Since the off-diagonal electrokinetic and thermo-electric 'distinct pathways' are central results, these uncertainties need to be propagated into the kernels and profiles; Figs. 2 and 3 currently show no error bars for the off-diagonal panels. At minimum, report uncertainties for those panels and restrict the pairwise 'distinct pathway' claims to channels where the signal exceeds the noise.
[SI Analytical reference models, Eqs. (S20)–(S28); Fig. 1C] The interpretation of the particle response as a 'hydrodynamic mode' relies on a two-parameter no-slip unsteady Stokes fit (H_eff and nu). A good fit to a flexible reference model does not by itself establish that the observed long-time tail is hydrodynamic, because the fitted parameters could absorb errors from the thermostat or from the Irving–Kirkwood current convention. Please provide an out-of-sample test, such as predicting the local–local G_nn(z,z') from the same fitted parameters, and report fit residuals as a function of z and t.

minor comments (5)

[Eq. (5)] In Eq. (5), the chain R_ab(r,r',t)=R†_ba(r',r,-t)=R†_ba(r',r,t) conflates stationarity with time-reversal symmetry; for cross-correlations the two relations are not redundant, and the chain as written implies R_ba(r',r,t)=R_ba(r',r,-t), which is not generally true. Please state the symmetry more carefully.
[Fig. 3 and SI Fig. S2] The color scales in the matrix plots are not defined: the main text says plotted quantities are rescaled for visualization, but the reader cannot determine zero levels, sign conventions, or amplitude ratios without consulting many separate captions. Please add explicit color bars and state the normalization for each panel.
[SI Materials and Methods, Extraction of response kernels] The uncertainty statement says errors are ±2 SE over the ensemble samples, but it is not clear whether the 95% confidence intervals include both replica variance and the two lateral directions as independent samples, nor whether block averaging over time is used. Please clarify the estimator.
[Table S2 caption] The caption gives units as [a][b]/(k_B T σ τ), but for charge entries involving e^2 the reader must infer e=1; please state explicitly that e=1 in reduced units.
[SI Eqs. (S46)–(S49)] The excess-flux transformation uses bulk densities ρ_bulk_s and ρ_bulk_h; please state explicitly whether these are evaluated at the pore center and discuss the sensitivity of the excess-basis conclusions to this choice.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: response kernels are direct equilibrium correlations; hydrodynamic and Nernst–Einstein references are post hoc fits, and self-citations are not load-bearing.

full rationale

The central object R_ab is defined in Eq. (4) directly as an equilibrium current correlation, and the projected quantities K_ab, M_ab, C_ab, and G_ab are obtained from those correlations by explicit time and space integrations (Eqs. S13–S19), with no fitted parameter entering the definition of the response kernels. The unsteady Stokes and Nernst–Einstein descriptions are introduced only as interpretive reference models: the effective confinement and viscosity are fitted to the already-computed spatiotemporal response (Materials and Methods, Fig. S1), and the paper explicitly states that the dashed lines are obtained by fitting, not by independent first-principles derivation. The excess-flux transformation is likewise presented as a representation-dependent diagnostic rather than as the source of the physical content. Self-citations (refs. 4, 8, 17, 23, 25) appear only as contextual support for prior methods and observations, and no uniqueness theorem or ansatz is imported from same-author prior work to force the chosen formulation. The stated limitations—thermostat damping, heat-current convention, linear-response and closed-system restrictions—are robustness or correctness concerns, not circular reductions. No load-bearing step in the derivation chain reduces by construction to its own inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper's central result is extracted directly from MD correlations, so the free-parameter burden is limited to the two hydrodynamic fit parameters used for interpretation. The key axioms are standard linear response, the Irving-Kirkwood current convention (with acknowledged non-uniqueness for heat), the thermostat assumption, and the fitted Stokes reference model. No new physical entities are introduced.

free parameters (2)

Effective confinement H_eff = 19.49 +/- 0.02 (reduced units)
Fitted to the unsteady Stokes model to match the spatiotemporal particle response M_nn(z,t); used to interpret the response as a hydrodynamic mode.
Effective kinematic viscosity nu = 1.465 +/- 0.005 (reduced units)
Fitted simultaneously with H_eff to the transient approach toward the stationary hydrodynamic profile; the identification of momentum transport as a hydrodynamic mode depends on this fit.

assumptions (5)

standard math Linear response theory: the response kernel equals the equilibrium current correlation function (Eq. 4).
Standard Kubo linear response for Hamiltonian dynamics; derived in SI Eq. S34-S41. Assumes weak perturbations and equilibrium initial state.
domain assumption Microscopic currents are defined by the Irving-Kirkwood construction, with a specific heat-current convention.
The heat current localization is not unique; the paper notes the heat kernels are convention-dependent (SI 'Thermodynamic force-flux conjugacy' and Limitations).
domain assumption The MD thermostat (Nosé-Hoover, damping 0.1) preserves the equilibrium dynamics relevant to transport correlations.
Strong damping may alter dynamics; the paper does not test thermostat dependence.
ad hoc to paper The unsteady Stokes model with fitted H_eff and nu is an adequate reference for labeling the particle response as hydrodynamic.
The model is fitted to the MD data; the hydrodynamic-mode interpretation is based on this fit (SI 'Hydrodynamic reference model').
ad hoc to paper The excess-flux transformation (SI Eq. S46) subtracts bulk advection using densities measured from the same simulation.
Choice of excess basis is diagnostic; the paper states it is not unique.

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Cite this review

Pith. "Pith review of Resolving coupled transport in space and time from molecular fluctuations in confined fluids." pith.science (2026). https://pith.science/paper/OVO24OCN

@misc{pith2026260804920,
  author       = {Pith},
  title        = {Pith review of: Resolving coupled transport in space and time from molecular fluctuations in confined fluids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OVO24OCN}},
  note         = {Machine review of arXiv:2608.04920}
}

read the original abstract

Transport in fluids is generally reduced to continuum laws parametrized by bulk coefficients and effective interfacial parameters, such as viscosities, diffusivities, slip lengths, and interfacial resistances. This description becomes incomplete at the nanoscale, where spatial heterogeneity, molecular structure, and finite relaxation times are inseparable from the transport process. Here we formulate coupled transport in nanoconfined fluids as a space--time-resolved Onsager response matrix and extract it from equilibrium molecular dynamics simulations. Applied to a confined charged fluid, the framework resolves the nonlocal and transient pathways coupling particle, solute, heat, and charge transport. Momentum transport appears as a long-lived, nonlocal hydrodynamic mode, whereas charge transport relaxes rapidly through localized ionic friction. Off-diagonal responses reveal distinct projected dynamics, providing a microscopic basis for nonlocal, history-dependent transport laws.

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Works this paper leans on

49 extracted references · 30 canonical work pages

[1]

R. B. Bird, W. E. Stewart, E. N. Lightfoot,Transport Phenomena(John Wiley & Sons, Hoboken, NJ), 2 ed. (2007)

work page 2007
[2]

J. D. Jackson,Classical electrodynamics(Wiley, New York, NY), 3rd ed. ed. (1999),http: //cdsweb.cern.ch/record/490457

work page 1999
[3]

R. G. Larson,The Structure and Rheology of Complex Fluids(Oxford University Press, New York) (1999)

work page 1999
[4]

Hoang Ngoc Minh, G

T. Hoang Ngoc Minh, G. Stoltz, B. Rotenberg, Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations.The Journal of Chemical Physics 158(10), 104103 (2023), doi:10.1063/5.0139258,https://doi.org/10.1063/5.0139258

doi:10.1063/5.0139258 2023
[5]

Bocquet, E

L. Bocquet, E. Charlaix, Nanofluidics, from bulk to interfaces.Chem. Soc. Rev.39, 1073–1095 (2010), doi:10.1039/B909366B,http://dx.doi.org/10.1039/B909366B

doi:10.1039/b909366b 2010
[6]

Simon, Y

P. Simon, Y. Gogotsi, Perspectives for electrochemical capacitors and related devices.Nat Mater19(11), 1151–1163 (2020)

work page 2020
[7]

M. Kleber,et al., Dynamic interactions at the mineral–organic matter interface.Nature Reviews Earth & Environment2(6), 402–421 (2021), doi:10.1038/s43017-021-00162-y,https:// doi.org/10.1038/s43017-021-00162-y

work page doi:10.1038/s43017-021-00162-y 2021
[8]

B. Wild, C. E. White, I. C. Bourg, Molecular Dynamics Simulations of Reverse Osmosis in Silica Nanopores.The Journal of Physical Chemistry C126(21), 9161–9172 (2022), doi: 10.1021/acs.jpcc.2c01815,https://doi.org/10.1021/acs.jpcc.2c01815

work page doi:10.1021/acs.jpcc.2c01815 2022

Show all 49 references

[9]

Kavokine, R

N. Kavokine, R. R. Netz, L. Bocquet, Fluids at the Nanoscale: From Continuum to Subcon- tinuum Transport.Annual Review of Fluid Mechanics53(Volume 53, 2021), 377–410 (2021), doi:https://doi.org/10.1146/annurev-fluid-071320-095958,https://www.annualreviews. org/content/journals...

2021 doi
[10]

Schlaich, J.-L

A. Schlaich, J.-L. Barrat, B. Coasne, Theory and Modeling of Transport for Simple Fluids in Nanoporous Materials: From Microscopic to Coarse-Grained Descriptions.Chemical Re- views125(5), 2561–2624 (2025), doi:10.1021/acs.chemrev.4c00406,https://doi.org/10. 1021/acs.chemrev.4c00406

2025 doi
[11]

R. Hartkamp,et al., Measuring surface charge: Why experimental characterization and molecular modeling should be coupled.Current Opinion in Colloid & Interface Sci- ence37, 101–114 (2018), doi:https://doi.org/10.1016/j.cocis.2018.08.001,https://www. sciencedirect.com/science/a...

2018 doi
[12]

Marbach, D

S. Marbach, D. S. Dean, L. Bocquet, Transport and dispersion across wiggling nanopores. Nature Physics14(11), 1108–1113 (2018), doi:10.1038/s41567-018-0239-0,https://doi. org/10.1038/s41567-018-0239-0

2018 doi
[13]

Kavokine, M.-L

N. Kavokine, M.-L. Bocquet, L. Bocquet, Fluctuation-induced quantum friction in nanoscale water flows.Nature602(7895), 84–90 (2022), doi:10.1038/s41586-021-04284-7,https: //doi.org/10.1038/s41586-021-04284-7

2022 doi
[14]

Yoshida, H

H. Yoshida, H. Mizuno, T. Kinjo, H. Washizu, J.-L. Barrat, Generic transport coefficients of a confined electrolyte solution.Phys. Rev. E90, 052113 (2014), doi:10.1103/PhysRevE.90. 052113,https://link.aps.org/doi/10.1103/PhysRevE.90.052113

2014 doi
[15]

Marbach, L

S. Marbach, L. Bocquet, Osmosis, from molecular insights to large-scale applications.Chem. Soc. Rev.48, 3102–3144 (2019), doi:10.1039/C8CS00420J,http://dx.doi.org/10.1039/ C8CS00420J

2019 doi
[16]

Helms, A

P. Helms, A. R. Poggioli, D. T. Limmer, Intrinsic Interface Adsorption Drives Selectivity in Atomically Smooth Nanofluidic Channels.Nano Letters23(10), 4226–4233 (2023), doi: 10.1021/acs.nanolett.3c00207,https://doi.org/10.1021/acs.nanolett.3c00207

2023 doi
[17]

Hoang Ngoc Minh, S

T. Hoang Ngoc Minh, S. Varghese, B. Rotenberg, Coupled concentration-charge dynamics in 1:1 electrolytes with unequal diffusion coefficients: Local transient response and fluctuations. The Journal of Chemical Physics164(19), 194109 (2026), doi:10.1063/5.0323816,https: //doi.or...

2026 doi
[18]

Zwanzig,Nonequilibrium Statistical Mechanics(Oxford University Press, New York) (2001)

R. Zwanzig,Nonequilibrium Statistical Mechanics(Oxford University Press, New York) (2001)

2001
[19]

te Vrugt, H

M. te Vrugt, H. L¨owen, R. Wittkowski, Classical dynamical density functional theory: from fun- damentals to applications.Advances in Physics69(2), 121–247 (2020), doi:10.1080/00018732. 2020.1854965,https://doi.org/10.1080/00018732.2020.1854965

2020
[20]

Franosch,et al., Resonances arising from hydrodynamic memory in Brownian motion

T. Franosch,et al., Resonances arising from hydrodynamic memory in Brownian motion. Nature478(7367), 85–88 (2011)

2011
[21]

Mangaud, B

E. Mangaud, B. Rotenberg, Sampling mobility profiles of confined fluids with equilibrium molecular dynamics simulations.The Journal of Chemical Physics153(4), 044125 (2020), doi:10.1063/5.0013952,https://doi.org/10.1063/5.0013952

2020 doi
[23]

T. R. Underwood, I. C. Bourg, Dielectric Properties of Water in Charged Nanopores.The Journal of Physical Chemistry B126(14), 2688–2698 (2022), doi:10.1021/acs.jpcb.1c09688, https://doi.org/10.1021/acs.jpcb.1c09688

2022 doi
[24]

T. S. Domingues, R. Coifman, A. Haji-Akbari, Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook.Journal of Chemical Theory and Computation20(11), 4427–4455 (2024), doi: 10.1021/acs.jctc.4c...

2024 doi
[25]

Hoang Ngoc Minh, B

T. Hoang Ngoc Minh, B. Rotenberg, S. Marbach, Ionic fluctuations in finite volumes: fractional noise and hyperuniformity.Faraday Discuss.246, 225–250 (2023), doi:10.1039/D3FD00031A, http://dx.doi.org/10.1039/D3FD00031A

2023 doi
[26]

E. K. R. Mackay, S. Marbach, B. Sprinkle, A. L. Thorneywork, The Counto- scope: Measuring Self and Collective Dynamics without Trajectories.Phys. Rev. X 16 14, 041016 (2024), doi:10.1103/PhysRevX.14.041016,https://link.aps.org/doi/10. 1103/PhysRevX.14.041016

2024 doi
[27]

Onsager, Reciprocal Relations in Irreversible Processes

L. Onsager, Reciprocal Relations in Irreversible Processes. I.Phys. Rev.37, 405–426 (1931), doi:10.1103/PhysRev.37.405,https://link.aps.org/doi/10.1103/PhysRev.37.405

1931 doi
[28]

S. R. Maduar, A. V. Belyaev, V. Lobaskin, O. I. Vinogradova, Electrohydrodynamics Near Hydrophobic Surfaces.Phys. Rev. Lett.114, 118301 (2015), doi:10.1103/PhysRevLett.114. 118301,https://link.aps.org/doi/10.1103/PhysRevLett.114.118301

2015 doi
[29]

Ganti, Y

R. Ganti, Y. Liu, D. Frenkel, Molecular Simulation of Thermo-osmotic Slip.Phys. Rev. Lett. 119, 038002 (2017), doi:10.1103/PhysRevLett.119.038002,https://link.aps.org/doi/ 10.1103/PhysRevLett.119.038002

2017 doi
[30]

Materials and methods are available as supplementary material
[31]

Hansen, I

J.-P. Hansen, I. R. McDonald,Theory of Simple Liquids(Academic Press, Amsterdam), 3 ed. (2006)

2006
[32]

Kubo, Statistical-Mechanical Theory of Irreversible Processes

R. Kubo, Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems.Journal of the Physical Society of Japan 12(6), 570–586 (1957), doi:10.1143/JPSJ.12.570

1957 doi
[33]

H. Shi, C. J. Mundy, G. K. Schenter, J. Chun, Incorporating the molecular-scale into a hydro- dynamic description of confined aqueous systems.The Journal of Chemical Physics163(13), 134708 (2025), doi:10.1063/5.0279626,https://doi.org/10.1063/5.0279626

2025 doi
[34]

M. Z. Bazant, K. Thornton, A. Ajdari, Diffuse-charge dynamics in electrochemical systems. Phys. Rev. E70, 021506 (2004), doi:10.1103/PhysRevE.70.021506,https://link.aps. org/doi/10.1103/PhysRevE.70.021506

2004 doi
[35]

K. D. Fong, J. Self, B. D. McCloskey, K. A. Persson, Ion Correlations and Their Impact on Transport in Polymer-Based Electrolytes.Macromolecules54(6), 2575–2591 (2021), doi: 10.1021/acs.macromol.0c02545,https://doi.org/10.1021/acs.macromol.0c02545. 17

2021 doi
[36]

Duque-Zumajo, J

D. Duque-Zumajo, J. A. de la Torre, P. Espa ˜nol, Non-local viscosity from the Green–Kubo formula.The Journal of Chemical Physics152(17), 174108 (2020), doi:10.1063/5.0006212, https://doi.org/10.1063/5.0006212

2020 doi
[37]

A. T. Bui, F. L. Thiemann, A. Michaelides, S. J. Cox, Classical Quantum Friction at Water– Carbon Interfaces.Nano Letters23(2), 580–587 (2023), doi:10.1021/acs.nanolett.2c04187, https://doi.org/10.1021/acs.nanolett.2c04187

2023 doi
[38]

A. T. Bui, S. J. Cox, Revisiting the Green–Kubo relation for friction in nanofluidics.The Journal of Chemical Physics161(20), 201102 (2024), doi:10.1063/5.0238363,https://doi.org/ 10.1063/5.0238363

2024 doi
[39]

Samm¨ uller, S

F. Samm¨ uller, S. Hermann, D. de las Heras, M. Schmidt, Neural functional theory for in- homogeneous fluids: Fundamentals and applications.Proceedings of the National Academy of Sciences120(50), e2312484120 (2023), doi:10.1073/pnas.2312484120,https://www. pnas.org/doi/abs/10....

2023 doi
[40]

Grmela, H

M. Grmela, H. C. ¨Ottinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism.Physical Review E56(6), 6620–6632 (1997), doi:10.1103/PhysRevE. 56.6620

1997 doi
[41]

S. P. Das, Mode-coupling theory and the glass transition in supercooled liquids.Rev. Mod. Phys. 76, 785–851 (2004), doi:10.1103/RevModPhys.76.785,https://link.aps.org/doi/10. 1103/RevModPhys.76.785

2004 doi
[42]

Donev, A

A. Donev, A. J. Nonaka, C. Kim, A. L. Garcia, J. B. Bell, Fluctuating hydrodynam- ics of electrolytes at electroneutral scales.Phys. Rev. Fluids4, 043701 (2019), doi:10. 1103/PhysRevFluids.4.043701,https://link.aps.org/doi/10.1103/PhysRevFluids. 4.043701

2019 doi
[43]

Schmidt, Power functional theory for many-body dynamics.Rev

M. Schmidt, Power functional theory for many-body dynamics.Rev. Mod. Phys.94, 015007 (2022), doi:10.1103/RevModPhys.94.015007,https://link.aps.org/doi/10. 1103/RevModPhys.94.015007. 18

2022 doi
[44]

A. Obliger, Simple and efficient algorithms based on Volterra equations to compute memory kernels and projected cross-correlation functions from molecular dynamics.The Journal of Chemical Physics158(14), 144101 (2023), doi:10.1063/5.0143707,https://doi.org/10. 1063/5.0143707

2023 doi
[45]

A. T. Bui, S. J. Cox, Dielectrocapillarity for exquisite control of fluids.Nature Communica- tions17(1), 2661 (2026), doi:10.1038/s41467-026-69482-1,https://doi.org/10.1038/ s41467-026-69482-1

2026 doi
[46]

T. M. Kamsma,et al., Brain-inspired computing with fluidic iontronic nanochannels.Proceed- ings of the National Academy of Sciences121(18), e2320242121 (2024), doi:10.1073/pnas. 2320242121,https://www.pnas.org/doi/abs/10.1073/pnas.2320242121

2024 doi
[47]

J. Z. Yang, X. Wu, X. Li, A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models.The Journal of Chemical Physics137(13), 134104 (2012), doi:10.1063/1.4755946,https://doi.org/10.1063/1.4755946

2012 doi
[48]

Ferreira de Souza, L

N. Ferreira de Souza, L. F. Mercier Franco, B. Coasne, Consistency of Equilibrium and Nonequilibrium Molecular Dynamics to Assess Thermal Conductivity.Journal of Chemical & Engineering Data71(3), 1022–1032 (2026), doi:10.1021/acs.jced.5c00628,https://doi. org/10.1021/acs.jced.5c00628

2026 doi
[49]

A. P. Thompson,et al., LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales.Comp. Phys. Comm.271, 108171 (2022), doi:10.1016/j.cpc.2021.108171

2022
[50]

J. J. Erpenbeck, Einstein-Kubo-Helfand and McQuarrie relations for transport coefficients. Phys. Rev. E51, 4296–4308 (1995), doi:10.1103/PhysRevE.51.4296,https://link.aps. org/doi/10.1103/PhysRevE.51.4296. 19 Acknowledgments We thank Princeton Research Computing for technical ...

1995 doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

R. B. Bird, W. E. Stewart, E. N. Lightfoot,Transport Phenomena(John Wiley & Sons, Hoboken, NJ), 2 ed. (2007)

work page 2007

[2] [2]

J. D. Jackson,Classical electrodynamics(Wiley, New York, NY), 3rd ed. ed. (1999),http: //cdsweb.cern.ch/record/490457

work page 1999

[3] [3]

R. G. Larson,The Structure and Rheology of Complex Fluids(Oxford University Press, New York) (1999)

work page 1999

[4] [4]

Hoang Ngoc Minh, G

T. Hoang Ngoc Minh, G. Stoltz, B. Rotenberg, Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations.The Journal of Chemical Physics 158(10), 104103 (2023), doi:10.1063/5.0139258,https://doi.org/10.1063/5.0139258

doi:10.1063/5.0139258 2023

[5] [5]

Bocquet, E

L. Bocquet, E. Charlaix, Nanofluidics, from bulk to interfaces.Chem. Soc. Rev.39, 1073–1095 (2010), doi:10.1039/B909366B,http://dx.doi.org/10.1039/B909366B

doi:10.1039/b909366b 2010

[6] [6]

Simon, Y

P. Simon, Y. Gogotsi, Perspectives for electrochemical capacitors and related devices.Nat Mater19(11), 1151–1163 (2020)

work page 2020

[7] [7]

M. Kleber,et al., Dynamic interactions at the mineral–organic matter interface.Nature Reviews Earth & Environment2(6), 402–421 (2021), doi:10.1038/s43017-021-00162-y,https:// doi.org/10.1038/s43017-021-00162-y

work page doi:10.1038/s43017-021-00162-y 2021

[8] [8]

B. Wild, C. E. White, I. C. Bourg, Molecular Dynamics Simulations of Reverse Osmosis in Silica Nanopores.The Journal of Physical Chemistry C126(21), 9161–9172 (2022), doi: 10.1021/acs.jpcc.2c01815,https://doi.org/10.1021/acs.jpcc.2c01815

work page doi:10.1021/acs.jpcc.2c01815 2022