22 May 2023
 | 22 May 2023
Status: this preprint is currently under review for the journal MR.

Monte-Carlo Analysis of Asymmetry in Three-Site Relaxation Exchange: Probing Detailed Balance

Bernhard Blümich, Matthew Parziale, and 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.

Bernhard Blümich et al.

Status: open (until 19 Jun 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on mr-2023-8', Tom Barbara, 25 May 2023 reply
    • AC1: 'Reply on CC1', Bernhard Bluemich, 27 May 2023 reply

Bernhard Blümich et al.

Bernhard Blümich et al.


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Short summary
Detailed balance is a principle that underlies some fundamental laws in physics. Motivated to analyze asymmetry in three-site NMR relaxation-exchange maps, 2D Monte-Carlo simulations of vacancy and gas diffusion were executed. They show that detailed balance is violated for a small fraction of molecules diffusing in confinement. This fraction exchanges coherently in circles between three relaxation pools. It is understood to be a manifestation of diffusion eigenmodes or diffusive resonance.