Hydrodynamic Black Holes, Bacterial Entropy Generation and Emergent Inverted Populations*

We have created an a microfluidic environment where there is "gravity" (funnels that pump bacteria that are motile) into an "event horizon"  (a streamline in a hydrodynamic flow field which sweeps the bacteria away) in analogy to black holes - regions of space- time where gravity is so strong that there is an event horizon.  We use a form of Shannon entropy to compute the local entropy generation of a bacterial population in the area around our hydrodynamic black hole. We show that at a critical cell density the bacterial population density collectively inverts itself radially and moves against the funnel gravity field, avoiding crossing the hydrodynamic event horizon.