  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.
