the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Monte-Carlo Analysis of Asymmetry in Three-Site Relaxation Exchange: Probing Detailed Balance
Bernhard Blümich
Matthew Parziale
Matthew Augustine
Abstract. The question is investigated if three-site diffusive relaxation exchange in thermodynamic equilibrium can lead to exchange maps, which are asymmetric for fluids confined to pores. Asymmetry reports circular flow of particles between the relaxation sites which disagrees with detailed balance according to which the particle exchange between any pair of sites must be balanced. Vacancy diffusion and gas diffusion of particles confined to two-dimensional pores were modeled in Monte-Carlo simulations. For each particle move in vacancy diffusion on a 2D checkerboard grid, one of the eight neighboring destination cells was identified on the basis the jump probability calculated from an empirical approximation of the free energy. Gas diffusion was simulated without thermodynamic interaction on a simulation grid which was up to 104 times finer than the particle diameter. It was found that up to 1 % of all particles moves coherently in closed paths. This motion is attributed to pore resonance corresponding to diffusion eigenmodes. The study shows that detailed balance of multi-site exchange does not apply for a small fraction of particles when the exchange is impacted by topological constraints.
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Bernhard Blümich et al.
Status: open (until 19 Jun 2023)
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CC1: 'Comment on mr-2023-8', Tom Barbara, 25 May 2023
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This kind of result reminds me of the history of molecular dynamics simulations and the surprising "result of long time tales". Not long ago I read some interesting things about this in
https://doi.org/10.1140/epjh/e2018-90027-5 which discusses the work of Berni Alder and company.
where the molecular dynamics (an alternative to monte carlo) showed that hydrodynamic modes were observed. And of course Einstein is invoked!
"Contrary to all expectations,
and to the universally held view, going back to the early studies by Einstein, that
molecular chaos would dominate the statistical behaviour of the system, leading to an
exponential decay of the correlation function in time, the motions actually computed
on the machines showed that this was not the case: molecules seemed to keep memory
of their previous states of motion for much longer than requested by the dominant,
Markov-like conceptualization. This, in turn, suggested the possibility of extending
down to the microscopic scale the hydrodynamic approach, a guiding line that would
be a dominant theme of Alder's following researches, and would be the main subject
of the lectures he delivered at Varenna in 1985"Citation: https://doi.org/10.5194/mr-2023-8-CC1 -
AC1: 'Reply on CC1', Bernhard Bluemich, 27 May 2023
reply
Tom, thanks for your grand statement. But in the end this work just takes a closer look at the role of the fluid-solid interface in a case where the interface noticeably affects the bulk behavior.
Citation: https://doi.org/10.5194/mr-2023-8-AC1
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AC1: 'Reply on CC1', Bernhard Bluemich, 27 May 2023
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Bernhard Blümich et al.
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Bernhard Blümich et al.
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