Quantifying configurational information for a stochastic particle in a flow-field

TL;DR

This paper develops theoretical tools using nonequilibrium statistical physics to quantify the information content of stochastic particles in flow-fields, highlighting the dominant role of strain and divergence over rotation.

Contribution

It introduces a novel framework to quantify information in stochastic flow systems, revealing the limited role of rotation and emphasizing the importance of strain and divergence.

Findings

Rotation contributes weakly to information content.

Strain and divergence dominate transport and information change.

Rotation's effect appears at higher orders in time.

Abstract

Flow-fields are ubiquitous systems that are able to transport vital signalling molecules necessary for system function. While information regarding the location and transport of such particles is often crucial, it is not well-understood how to quantify the information in such stochastic systems. Using the framework of nonequilibrium statistical physics, we develop theoretical tools to address this question. We observe that rotation in a flow-field does not explicitly appear in the generalized potential that governs the rate of system entropy production. Specifically, in the neighborhood of a flow-field, rotation contributes to the information content only in the presence of strain -- and then with a comparatively weaker contribution than strain and at higher orders in time. Indeed, strain and especially the flow divergence, contribute most strongly to transport properties such as particle residence time and the rate of information change. These results shed light on how information can be analyzed and controlled in complex artificial and living flow-based systems.