Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning
Abstract
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 does not assume prior familiarity with these topics, and begins with principles originating from physics.
Related
- Optimizing optimal transport: Role of final distributions in finite-time thermodynamics
- Transport Determines Spectral Distance in Mesoscopic Thermodynamics
- Quantum Thermodynamics of Electron Transport along Chains of Redox Centers
- First law of thermodynamics for interacting charged black holes and applications
- A Novel q-Derivative Framework with Applications to q-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits
BibTeX
@misc{blumenthal2026bridging,
title = {{Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning}},
author = {Emmy Blumenthal and Nikolas Claussen and Benjamin Eysenbach and Catherine Ji and Gautam Reddy and Colin Scheibner and Benjamin Sorkin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15897},
eprint = {2609.15897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15897},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning
AU - Emmy Blumenthal
AU - Nikolas Claussen
AU - Benjamin Eysenbach
AU - Catherine Ji
AU - Gautam Reddy
AU - Colin Scheibner
AU - Benjamin Sorkin
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15897
UR - https://arxiv.org/abs/2609.15897
AB - 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 does not assume prior familiarity with these topics, and begins with principles originating from physics.
ER -