Well, a significant portion of empirical neuroscience works under the assumption that parts of the brain operate according to a predictive coding scheme, and there are countless studies that support this notion.
As predictive coding is a form of free energy minimization (under Gaussian assumptions), this implicitly provides empirical evidence.
As for the request to test the idea on live neurons, "In vitro neural networks minimise variational free energy" [1]
As predictive coding is a form of free energy minimization (under Gaussian assumptions), this implicitly provides empirical evidence.
As for the request to test the idea on live neurons, "In vitro neural networks minimise variational free energy" [1]
https://www.biorxiv.org/content/early/2018/05/16/323550