If I understand you correctly, the approach of statistical phyisics is reductionist and top-down. But do brains work in a top-down way? Do the properties of their parts explain the workings of the whole?
The little I have read and understood about the subject says that the salient features of the brain are represented by the interactions between their parts. In other words, not only the stimulus (cause), but also the internal state determines the response (effect). These internal states generate unpredictability and novelty. In such circumstances it is hard to find causal relations.