The energy has to “flow” throughout the system, from the input, and then eventually “dissipate”. That sets up a pattern of behavior/dynamics very different from equilibrium systems, where there are no such “coherent” flows.

As an example of the practical consequences of non-equilibrium, look up a recent HN discussions (couple of days ago) on how hot water could freeze faster than cold water.

That’s just homeostasis, which is an equilibrium state, sometimes described as dynamic equilibrium. Encyclopaedia Britannica, Oxford and Merriam Webster describe it as a form of Equilibrium. Wikipedia links to Homeostasis from the master page on Equilibrium and references it in its description. I don’t see how this is in contention.

Uh, not quite. Dynamic equilibrium (Eg: during chemical reactions) means something very specific & constrained, and doesn’t include any steady influx/outflux of energy, material, etc. On top of that, one can have not just flows, but also active regulation mechanisms which maintain homeostasis, possibly with periodic temporal behavior (which can never happen in “equilibrium”). So even though “equilibrium” and “dynamic” as English words might seem somewhat descriptive of homeostasis, I think the physics concept of “dynamic equilibrium” is distinct enough to be worth not conflating. Eg: entropy can be constant in a system in dynamical equilibrium, but (to our best understanding) homeostasis always generates entropy.