I'm fairly sure this is already in the usual canon of statistical mechanics.
"When one compares a hotplate with and without a Benard cell apparatus on top, there is an overall increase in entropy as energy passes through the system as required by the second law, because the increase in entropy in the environment (at the heat sink) is greater than the decreases in entropy that come about by maintaining gradients within the Benard cell system."
*I don't want to say "entropy" because it's not clear to many folks, including experts, whether entropy is uh, "correlated" or "anticorrelated" with complexity.
"When one compares a hotplate with and without a Benard cell apparatus on top, there is an overall increase in entropy as energy passes through the system as required by the second law, because the increase in entropy in the environment (at the heat sink) is greater than the decreases in entropy that come about by maintaining gradients within the Benard cell system."