Uncertainty relations and fluctuation theorems for Bayes nets
Statistical Mechanics
2025-09-01 v6 Machine Learning
Machine Learning
Abstract
Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP)of arbitrary sets of the systems in such a Bayes net. I also derive ``conditional'' fluctuation theorems, governing the distribution of EP in one set of systems conditioned on the EP of a different set of systems. I then derive thermodynamic uncertainty relations relating the EP of the overall system to the precisions of probability currents within the individual systems.
Cite
@article{arxiv.1911.02700,
title = {Uncertainty relations and fluctuation theorems for Bayes nets},
author = {David H. Wolpert},
journal= {arXiv preprint arXiv:1911.02700},
year = {2025}
}
Comments
5 pages main text, 10 pages appendices, 2 figures - more typos fixed from published version