# Bayesian Mechanics for Stationary Processes

arXiv: https://arxiv.org/abs/2106.13830 · HTML: https://mlsanity.com/paper/2106.13830/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2021.

## Built on by (most cited first, 10 of 10)

- [Designing Ecosystems of Intelligence from First Principles](https://mlsanity.com/paper/2212.01354/) (2022)
- [Interpreting systems as solving POMDPs: a step towards a formal understanding of agency](https://mlsanity.com/paper/2209.01619/) (2022)
- [Designing explainable artificial intelligence with active inference: A framework for transparent introspection and decision-making](https://mlsanity.com/paper/2306.04025/) (2023)
- [Interpreting Dynamical Systems as Bayesian Reasoners](https://mlsanity.com/paper/2112.13523/) (2021)
- [Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents](https://mlsanity.com/paper/2203.10592/) (2022)
- [A "good regulator theorem" for embodied agents](https://mlsanity.com/paper/2508.06326/) (2025)
- [Possible Principles for Aligned Structure Learning Agents](https://mlsanity.com/paper/2410.00258/) (2024)
- [A Mathematical Walkthrough and Discussion of the Free Energy Principle](https://mlsanity.com/paper/2108.13343/) (2021)
- [Mapping Husserlian phenomenology onto active inference](https://mlsanity.com/paper/2208.09058/) (2022)
- [Inferring Affective Consciousness in an Artificial Agent: A Case Study](https://mlsanity.com/paper/2609.03883/) (2026)

## Abstract (arXiv)

This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information about external states. Second, we introduce dynamics and represent adaptive systems as Markov blankets at steady-state. This allows us to identify a wide class of systems whose internal states appear to infer external states, consistent with variational inference in Bayesian statistics and theoretical neuroscience. Finally, we partition the blanket into sensory and active states. It follows that active states can be seen as performing active inference and well-known forms of stochastic control (such as PID control), which are prominent formulations of adaptive behaviour in theoretical biology and engineering.