# Path integrals, particular kinds, and strange things

arXiv: https://arxiv.org/abs/2210.12761 · HTML: https://mlsanity.com/paper/2210.12761/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2022.

## Built on by (most cited first, 20 of 20)

- [Expected Free Energy-based Planning as Variational Inference](https://mlsanity.com/paper/2504.14898/) (2025)
- [Are Biological Systems More Intelligent Than Artificial Intelligence?](https://mlsanity.com/paper/2405.02325/) (2024)
- [Active Inference and Intentional Behaviour](https://mlsanity.com/paper/2312.07547/) (2023)
- [Value of Information and Reward Specification in Active Inference and POMDPs](https://mlsanity.com/paper/2408.06542/) (2024)
- [Hybrid Life: Integrating Biological, Artificial, and Cognitive Systems](https://mlsanity.com/paper/2212.00285/) (2022)
- [Temporal Dynamics of Emotion and Cognition in Human Translation: Integrating the Task Segment Framework and the HOF Taxonomy](https://mlsanity.com/paper/2405.03111/) (2024)
- [Possible Principles for Aligned Structure Learning Agents](https://mlsanity.com/paper/2410.00258/) (2024)
- [Active inference and artificial reasoning](https://mlsanity.com/paper/2512.21129/) (2025)
- [Minimal Computational Preconditions for Subjective Perspective in Artificial Agents](https://mlsanity.com/paper/2602.02902/) (2026)
- [Why Is Anything Conscious?](https://mlsanity.com/paper/2409.14545/) (2024)
- [Self-orthogonalizing attractor neural networks emerging from the free energy principle](https://mlsanity.com/paper/2505.22749/) (2025)
- [Active Inference for Physical AI Agents -- An Engineering Perspective](https://mlsanity.com/paper/2603.20927/) (2026)
- [Influence of the Geometry of the world model on Curiosity Based Exploration](https://mlsanity.com/paper/2304.00188/) (2023)
- [Life-inspired Interoceptive Artificial Intelligence for Autonomous and Adaptive Agents](https://mlsanity.com/paper/2309.05999/) (2023)
- [The Phenomenology of Machine: A Comprehensive Analysis of the Sentience of the OpenAI-o1 Model Integrating Functionalism, Consciousness Theories, Active Inference, and AI Architectures](https://mlsanity.com/paper/2410.00033/) (2024)
- [On the Variational Costs of Changing Our Minds](https://mlsanity.com/paper/2509.17957/) (2025)
- [Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems](https://mlsanity.com/paper/2601.14096/) (2026)
- [Design, Cups, and Blankets. A Free-Energy-Principle-Based Approach to Product Design](https://mlsanity.com/paper/2604.22902/) (2026)
- [Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts](https://mlsanity.com/paper/2605.00604/) (2026)
- [Expected Free Energy-based Planning as Variational Inference](https://mlsanity.com/paper/2606.20658/) (2026)

## Abstract (arXiv)

This paper describes a path integral formulation of the free energy principle. The ensuing account expresses the paths or trajectories that a particle takes as it evolves over time. The main results are a method or principle of least action that can be used to emulate the behaviour of particles in open exchange with their external milieu. Particles are defined by a particular partition, in which internal states are individuated from external states by active and sensory blanket states. The variational principle at hand allows one to interpret internal dynamics - of certain kinds of particles - as inferring external states that are hidden behind blanket states. We consider different kinds of particles, and to what extent they can be imbued with an elementary form of inference or sentience. Specifically, we consider the distinction between dissipative and conservative particles, inert and active particles and, finally, ordinary and strange particles. Strange particles can be described as inferring their own actions, endowing them with apparent autonomy or agency. In short - of the kinds of particles afforded by a particular partition - strange kinds may be apt for describing sentient behaviour.