pith. sign in

arxiv: 2306.14723 · v1 · submitted 2023-06-26 · ❄️ cond-mat.mes-hall

Noise and fluctuations in nanoscale gas flow

J. Dastoor , D. M. Willerton , W. Reisner , G. Gervais This is my paper

Pith reviewed 2026-05-24 08:23 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords noisefluctuationsnanoscale gas flowquantum regimecumulant generating functionthermal noiseshot noisemass flow
0
0 comments X

The pith

Fundamental noise in nanoscale gas flow is calculated in classical and quantum regimes and shown to be analogous to electrical noise.

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

The paper calculates the basic noise present in dilute gas flowing through channels, both in ordinary classical conditions and in the quantum regime where Fermi-Dirac and Bose-Einstein statistics apply. For a two-terminal setup the quantum noise appears as a function of thermal and shot contributions, with thermal noise taking over when temperature greatly exceeds the pressure difference scaled by particle mass. The work also derives the cumulant generating function for mass flow and extracts the third cumulant from it. A sympathetic reader would care because these expressions supply a concrete way to predict fluctuations in tiny fluidic channels, extending the same logic that noise analysis provides for electronic circuits.

Core claim

The quantum noise for a two-terminal gaseous flow system is a complicated function of the thermal and shot noise, with the thermal noise dominating when 2 k_B T >> m ΔP and vice versa. The cumulant generating function for mass flow is derived and used to obtain an expression for the third cumulant of flow across a fluidic channel. These results hold in both classical and degenerate quantum regimes and are analogous to their electrical counterparts.

What carries the argument

The cumulant generating function for mass flow, which generates all higher-order statistics of the mass-flow distribution.

If this is right

  • Noise in fluidic channels can be predicted from separate thermal and shot contributions that switch dominance at a known temperature-pressure boundary.
  • The third cumulant expression supplies a measurable signature of flow asymmetry or non-Gaussian statistics.
  • The same two-terminal geometry and generating-function approach used for electrons can be applied directly to mass transport.
  • Results remain valid only while the gas stays dilute enough for standard quantum distributions to hold.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These formulas could be used to design low-fluctuation nanoscale fluidic sensors or pumps.
  • The same cumulant approach might be tested on other mesoscopic transport problems such as heat or particle flow.
  • Experimental checks in real channels would also reveal how quickly the dilute-gas assumption breaks down.

Load-bearing premise

The gaseous flow remains dilute enough that the Fermi-Dirac and Bose-Einstein distributions apply directly without additional interactions or boundary effects.

What would settle it

Measure the noise spectrum or third cumulant in a nanoscale channel while varying temperature and pressure difference, and check whether thermal noise dominates above the threshold 2 k_B T = m ΔP.

Figures

Figures reproduced from arXiv: 2306.14723 by D. M. Willerton, G. Gervais, J. Dastoor, W. Reisner.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The ratio of thermal noise to shot noise [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The root mean square (RMS) mass flow fluctuations [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We theoretically calculate the fundamental noise that is present in gaseous (dilute fluid) flow in channels in the classical and degenerate quantum regime, where the Fermi-Dirac and Bose- Einstein distribution must be considered. Results for both regimes are analogous to their electrical counterparts. The quantum noise is calculated for a two terminal system and is a complicated function of the thermal and shot noise with the thermal noise dominating when $2k_BT >> m\Delta P$ and vice versa. The cumulant generating function for mass flow, which generates all the higher order statistics related to our mass flow distribution, is also derived and is used to find an expression for the third cumulant of flow across a fluidic channel.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript theoretically calculates the fundamental noise present in gaseous (dilute fluid) flow through channels in the classical and degenerate quantum regimes, employing Fermi-Dirac and Bose-Einstein distributions. For a two-terminal system the quantum noise is obtained as a function of thermal and shot contributions, with the thermal term dominating when 2k_B T ≫ m ΔP; the cumulant generating function for mass flow is derived and used to obtain an explicit expression for the third cumulant.

Significance. If the central derivations are valid under the dilute-gas premise, the results would furnish a direct fluidic counterpart to mesoscopic electrical noise, including higher-order statistics, with potential relevance to fluctuation spectroscopy in nanoscale channels.

major comments (1)
  1. [Abstract] Abstract: the noise formula and the stated crossover condition 2k_B T ≫ m ΔP rest on the direct insertion of equilibrium Fermi-Dirac/Bose-Einstein distributions into a two-terminal Landauer-like construction. No explicit check or limiting argument is supplied showing that boundary scattering, finite Knudsen number, or interaction corrections leave the occupation factors and effective chemical-potential drop unaltered; this assumption is load-bearing for both the noise expression and the third-cumulant result.
minor comments (1)
  1. The abstract asserts that results are 'analogous to their electrical counterparts' but supplies neither the explicit mapping nor any discussion of differences arising from the use of mass flow rather than charge current.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the noise formula and the stated crossover condition 2k_B T ≫ m ΔP rest on the direct insertion of equilibrium Fermi-Dirac/Bose-Einstein distributions into a two-terminal Landauer-like construction. No explicit check or limiting argument is supplied showing that boundary scattering, finite Knudsen number, or interaction corrections leave the occupation factors and effective chemical-potential drop unaltered; this assumption is load-bearing for both the noise expression and the third-cumulant result.

    Authors: Our theoretical framework is developed under the dilute-gas premise, which by definition implies negligible particle interactions and a ballistic transport regime (large Knudsen number) through the nanoscale channel. In this setup, the two terminals act as reservoirs with equilibrium distributions (Fermi-Dirac or Bose-Einstein), and the pressure difference ΔP translates to a difference in chemical potential. The Landauer-like construction incorporates boundary scattering via the energy-dependent transmission probability. We acknowledge that the manuscript would benefit from an explicit statement of these assumptions. We will revise the text to include a dedicated paragraph discussing the validity of the model in the dilute, ballistic limit, thereby addressing the load-bearing nature of this assumption for the noise and cumulant results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations from standard distributions are self-contained

full rationale

The paper derives quantum noise and cumulant generating function for mass flow by direct application of Fermi-Dirac and Bose-Einstein distributions to a two-terminal setup, yielding expressions analogous to electrical noise with a stated crossover condition. No load-bearing steps reduce by construction to fitted parameters, self-citations, or ansatze imported from prior author work; the central results follow from the input distributions without renaming known results or self-definitional loops. The dilute-gas premise is an assumption but does not create circularity in the derivation chain itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the direct applicability of Fermi-Dirac and Bose-Einstein statistics to dilute gas flow in channels and the validity of the two-terminal analogy to electrical systems; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Fermi-Dirac and Bose-Einstein distributions apply to the dilute gaseous flow in the quantum regime
    Invoked in the abstract for the quantum noise calculation
  • domain assumption The system can be modeled as a two-terminal setup for noise calculations
    Stated for the quantum noise calculation in the abstract

pith-pipeline@v0.9.0 · 5650 in / 1262 out tokens · 20521 ms · 2026-05-24T08:23:45.129209+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages

  1. [1]

    Bao B, Riordon J, Mostowfi F and Sinton D 2017 Microfluidic and nanofluidic phase behaviour characterization for industrial CO2, oil and gas Lab Chip 17 2740-2759

    work page 2017

  2. [2]

    Gruener S and Huber P 2008 Knudsen Diffusion in Silcon Nanochannels Phys. Rev. Lett. 100, 064502

    work page 2008

  3. [3]

    Savard M, Tremblay-Darveau C and Gervais G 2009 Flow Conductance of a Single Nanohole Phys. Rev. Lett. 103, 104502

    work page 2009

  4. [4]

    Velasco A E, Friedman S G, Pevarnik M, Siwy Z S and Taborek P 2012 Pressure-driven flow through a single nanopore Phys. Rev. E 86, 025302

    work page 2012

  5. [5]

    Duc P-F, Savard M, Petrescu M, Rosenow B, Del Maestro A, and Gervais G 2015 Critical flow and dissipation in a quasi–one-dimensional superfluid Sci. Adv. 1, e140022

    work page 2015

  6. [6]

    Kulchytskyy B, Gervais G, and Del Maestro A 2013 Local Superfluidity at the nanoscale Phys. Rev. B 88, 064512

    work page 2013

  7. [7]

    Qian J, Wu H and Wang F 2023 Molecular geometry effect on gas transport through nanochannels: Beyond Knudsen theory App. Surf. Sci. 611, 155613

    work page 2023

  8. [8]

    Joshi R K, Carbone P, Wang F C, Kravets V G, Su Y, Grigorieva I V, Wu H A, Geim A K and Nair R R 7 2014 Precise and Ultrafast Molecular Sieving Through Graphene Oxide Membranes Science 343, 752

    work page 2014

  9. [9]

    Ding L, Wei Y, Li L, Zhang T, Wang H, Xue J, Ding L- X, Wang S, Caro J and Gogots Y 2018 MXene molecular sieving membranes for highly efficient gas separationNat. Comm. 9, 155

    work page 2018

  10. [10]

    Li H, Qiu C, Ren S, Dong Q, Zhang Z, Zhou F, Liang X, Wang J, Li S and Yu M 2020 Na+-gated water- conducting nanochannels for boosting CO2 conversion to liquid fuels Science 367, 667-671

    work page 2020

  11. [11]

    Scorrano G, Bruno G, Di Trani N, Ferrari M, Pimpinelli A and Grattoni A 2018 Gas Flow at the Ultra- nanoscale: Universal Predictive Model and Validation in Nanochannels of ˚Angstrom-Level Resolution ACS Appl Mater Interfaces 10(38), 32233-32238

    work page 2018

  12. [12]

    Shen W, Song F, Hu X, Zhu G and Zhu W 2019 Experimental study on flow characteristics of gas transport in micro- and nanoscale pores Scientific Reports textbf9, 10196

    work page 2019

  13. [13]

    Martin T and Landauer R 1992 Wave-packet approach to noise in multichannel mesoscopic systems Phys. Rev. B 45, 1742

    work page 1992

  14. [14]

    Feng J, Ilo-Okeke E O, Pyrkov A N, Askitopoulos A, and Byrnes T 2021 Sensitive detection of entanglement in exciton-polariton condensates via spin squeezing Phys. Rev. A 104, 013318

    work page 2021

  15. [15]

    Saminadayar L, Glattli D C, Jin Y, and Etienne B 1997 Observation of the e/3 Fractionally Charged Laughlin Quasiparticle Phys. Rev. Lett. 79, 2526

    work page 1997

  16. [16]

    de-Picciotto R, Reznikov M, Heiblum M, Umansky V, Bunin G, and Mahalu D 1997 Direct observation of a fractional charge Nature 389, 162

    work page 1997

  17. [17]

    Obot N T 2002 Toward a better understanding of friction and heat/mass transfer in microchannels– a literature review Microscale Thermophysical Engineering 6:3, 155- 173

    work page 2002

  18. [18]

    Morini G L, Lorenzini M, et al 2009 Analysis of laminar-to-turbulent transition for isothermal gas flows in microchannels Microfluid Nanofluid 7, 181-190

    work page 2009

  19. [19]

    of the ASME 2003 1st Int

    Celata G P 2003 Single-Phase Heat Transfer and Fluid Flow in Micropipes Proc. of the ASME 2003 1st Int. Conf. on Microchannels and Minichannels April 24-25, p 171-179

    work page 2003

  20. [20]

    Gogoi G, Reddy K A, and Mondal P K 2021 Electro- osmotic flow through nanochannel with different surface charge configurations: A molecular dynamics simulation study, Physics of Fluids 33, 092115

    work page 2021

  21. [21]

    Annual Review of Fluid Mechanics53, 377-410

    Kavokine N, Netz R R, and Bocquet L, and Netz R 2021 Fluids at the Nanoscale: From Continuum to Subcontinuum Transport. Annual Review of Fluid Mechanics53, 377-410

    work page 2021

  22. [22]

    Lambert G, Gervais G, and Mullin W J 2008 Quantum- limited mass flow of liquid 3He Low Temp. Phys. textbf34, 249

    work page 2008

  23. [23]

    Krinner, D

    S. Krinner, D. Stadler, D. Husmann, J. Brantut, and T. Esslinger, Observation of quantized conductance in neutral matter, Nature 517, 64 (2015)

    work page 2015

  24. [24]

    Isakov S B, Martin T, and Ouvry S 1999 Conductance and Shot Noise for Particles with Exclusion Statistics Phys. Rev. Lett. 83, 580

    work page 1999

  25. [25]

    Nyquist H 1928 Thermal Agitation of Electric Charge in Conductors Phys. Rev. 32, 110

    work page 1928

  26. [26]

    van der Ziel A 1978 Limiting Noise in solid state devices Noise In Physical Systems (Berlin: Springer). p 2-12

    work page 1978

  27. [27]

    Schottky W 1918 ¨Uber spontane Stromschwankungen in verschiedenen Elektrizit¨ atsleiternAnn. Phys. 362, 541

    work page 1918

  28. [28]

    Levitov L S 2003 The statistical theory of mesoscopic noise Quantum Noise in Mesoscopic Physics (Dordrecht: Springer) p 373-396

    work page 2003

  29. [29]

    Zakka-Bajjani E, S´ egala J, Portier F, Roche P, Glattli D C, Cavanna A, and Jin Y 2007 Experimental Test of the High-Frequency Quantum Shot Noise Theory in a Quantum Point Contact Phys. Rev. Lett. 99, 236803

    work page 2007

  30. [30]

    Qian J, Li Y, Wu H and Wang F 2021 Surface morphological effects on gas transport through nanochannels with atomically smooth walls Carbon 180, 85-91

    work page 2021

  31. [31]

    Holt J K, Park H G, Wang Y, Stadermann M, Artyukhin A B, Grigoropoulos C P, Noy A and Bakajin O 2006 Fast Mass Transport ThroughSub–2-Nanometer Carbon Nanotubes Science 312, 1034-1037

    work page 2006

  32. [32]

    Keerthi A, Geim A K, Janardanan A, Rooney A P, Esfandiar A, Hu S, Dar S A, Grigorieva I V, Haigh S J, Wang F C and Radha B 2018 Ballistic molecular transport through two-dimensional channels Nature 558, 420-424

    work page 2018

  33. [33]

    Liang S, Xiang F, et al 2020 Noise in nanopore sensors: Sources, models, reduction, and benchmarking Nanotechnology and Precision Engineering 3, 9

    work page 2020