Malgaretti P, Harting J. Closed Formula for Transport across Constrictions.
ENTROPY (BASEL, SWITZERLAND) 2023;
25:470. [PMID:
36981357 PMCID:
PMC10047801 DOI:
10.3390/e25030470]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Revised: 03/01/2023] [Accepted: 03/05/2023] [Indexed: 06/18/2023]
Abstract
In the last decade, the Fick-Jacobs approximation has been exploited to capture transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show that, for fore-aft symmetric channels, the flux of noninteracting systems is fully captured by its linear response regime. For this case, we derive a very simple formula that captures the correct trends and can be exploited as a simple tool to design experiments or simulations. Lastly, we show that higher-order corrections in the flux may appear for nonsymmetric channels.
Collapse