  The concept of free energy has its origins in 19th century thermodynamics,
but has recently found its way into the behavioral and neural sciences, where
it has been promoted for its wide applicability and has even been suggested as
a fundamental principle of understanding intelligent behavior and brain
function. We argue that there are essentially two different notions of free
energy in current models of intelligent agency, that can both be considered as
applications of Bayesian inference to the problem of action selection: one that
appears when trading off accuracy and uncertainty based on a general maximum
entropy principle, and one that formulates action selection in terms of
minimizing an error measure that quantifies deviations of beliefs and policies
from given reference models. The first approach provides a normative rule for
action selection in the face of model uncertainty or when information
processing capabilities are limited. The second approach directly aims to
formulate the action selection problem as an inference problem in the context
of Bayesian brain theories, also known as Active Inference in the literature.
We elucidate the main ideas and discuss critical technical and conceptual
issues revolving around these two notions of free energy that both claim to
apply at all levels of decision-making, from the high-level deliberation of
reasoning down to the low-level information processing of perception.
