# The Two Kinds of Free Energy and the Bayesian Revolution

arXiv: https://arxiv.org/abs/2004.11763 · HTML: https://mlsanity.com/paper/2004.11763/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2020.

## Built on by (most cited first, 7 of 7)

- [A maximum entropy model of bounded rational decision-making with prior beliefs and market feedback](https://mlsanity.com/paper/2102.09180/) (2021)
- [Value of Information and Reward Specification in Active Inference and POMDPs](https://mlsanity.com/paper/2408.06542/) (2024)
- [Factorised Active Inference for Strategic Multi-Agent Interactions](https://mlsanity.com/paper/2411.07362/) (2024)
- [Distributionally Robust Free Energy Principle for Decision-Making](https://mlsanity.com/paper/2503.13223/) (2025)
- [Stochastic Surprisal: An inferential measurement of Free Energy in Neural Networks](https://mlsanity.com/paper/2302.05776/) (2023)
- [Prior preferences in active inference agents: soft, hard, and goal shaping](https://mlsanity.com/paper/2512.03293/) (2025)
- [A Semantic Generalization of Shannon's Information Theory and Applications](https://mlsanity.com/paper/2510.15871/) (2025)

## Abstract (arXiv)

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.