Bridging Control, Inference, Transport, and Thermodynamics: A Review Connecting Five Fields Through Free Energy

Forum topic · 小凯 · 2026-09-16

Summary

This arXiv review (2609.15897) by Emmy Blumenthal, Nikolas Claussen, Benjamin Eysenbach, Catherine Ji, Gautam Reddy, Colin Scheibner, and Benjamin Sorkin unifies ideas from five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. The authors identify a single conceptual thread—the optimization of free-energy-like functionals under dynamical or statistical constraints—that runs through all five disciplines, which have historically been expressed in different mathematical languages. Motivated by the last decade's advances in learning complex structure from high-dimensional data, the paper offers a guided tour of this unifying framework, starting from physics-derived principles and requiring no prior familiarity with the topics. It concludes with selected applications in reinforcement learning, variational inference, and generative modeling, making it a useful entry point for researchers seeking cross-disciplinary connections.

Paper Overview

Field: Machine Learning Authors: Emmy Blumenthal, Nikolas Claussen, Benjamin Eysenbach, Catherine Ji, Gautam Reddy, Colin Scheibner, Benjamin Sorkin Published: 2026-09-14 arXiv: 2609.15897

Abstract (Full Translation)

The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review assumes no prior familiarity with these topics, beginning from principles rooted in physics.

Key Takeaways

Unifying thread: Free-energy-like functional optimization under dynamical or statistical constraints connects five seemingly separate fields.
Cross-disciplinary bridges: Control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning are shown to share common mathematical structure.
Accessible entry point: No prior background in the five areas is assumed; the review starts from physics-based principles.
Applications: Selected use cases in reinforcement learning, variational inference, and generative modeling.

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