The free energy principle is a mathematical principle of information physics. Its application to fMRI brain imaging data as a theoretical framework suggests that the brain reduces surprise or uncertainty by making predictions based on internal models and uses sensory input to update its models so as to improve the accuracy of its predictions. This principle approximates an integration of Bayesian inference with active inference, where actions are guided by predictions and sensory feedback refines them. From it, wide-ranging inferences have been made about brain function, perception, and action. Its applicability to living systems has been questioned.

In biophysics and cognitive science, the free energy principle is a mathematical principle describing a formal account of the representational capacities of physical systems: that is, why things that exist look as if they track properties of the systems to which they are coupled. It establishes that the dynamics of physical systems minimise a quantity known as surprisal (which is the negative log probability of some outcome); or equivalently, its variational upper bound, called free energy. The principle is used especially in Bayesian approaches to brain function, but also some approaches to artificial intelligence; it is formally related to variational Bayesian methods and was originally introduced by Karl Friston as an explanation for embodied perception-action loops in neuroscience.

The free energy principle models the behaviour of systems that are distinct from, but coupled to, another system (e.g., an embedding environment), where the degrees of freedom that implement the interface between the two systems is known as a Markov blanket. More formally, the free energy principle says that if a system has a "particular partition" (i.e., into particles, with their Markov blankets), then subsets of that system will track the statistical structure of other subsets (which are known as internal and external states or paths of a system).

The free energy principle is based on the Bayesian idea of the brain as an "inference engine." Under the free energy principle, systems pursue paths of least surprise, or equivalently, minimize the difference between predictions based on their model of the world and their sense and associated perception. This difference is quantified by variational free energy and is minimized by continuous correction of the world model of the system, or by making the world more like the predictions of the system. By actively changing the world to make it closer to the expected state, systems can also minimize the free energy of the system. Friston assumes this to be the principle of all biological reaction. Friston also believes his principle applies to mental disorders as well as to artificial intelligence. AI implementations based on the active inference principle have shown advantages over other methods.

The free energy principle is a mathematical principle of information physics: much like the principle of maximum entropy or the principle of least action, it is true on mathematical grounds. To attempt to falsify the free energy principle is a category mistake, akin to trying to falsify calculus by making empirical observations. (One cannot invalidate a mathematical theory in this way; instead, one would need to derive a formal contradiction from the theory.) In a 2018 interview, Friston explained what it entails for the free energy principle to not be subject to falsification:

I think it is useful to make a fundamental distinction at this point—that we can appeal to later.

The distinction is between a state and process theory; i.e., the difference between a normative principle that things may or may not conform to, and a process theory or hypothesis about how that principle is realized. Under this distinction, the free energy principle stands in stark distinction to things like predictive coding and the Bayesian brain hypothesis. This is because the free energy principle is what it is — a principle. Like Hamilton's principle of stationary action, it cannot be falsified. It cannot be disproven. In fact, there's not much you can do with it, unless you ask whether measurable systems conform to the principle. On the other hand, hypotheses that the brain performs some form of Bayesian inference or predictive coding are what they are—hypotheses. These hypotheses may or may not be supported by empirical evidence.

There are many examples of these hypotheses being supported by empirical evidence.