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.

D. Wolpert, Uncertainty relations and fluctuation theorems for Bayes nets, Physical Review Letters 125 (2020) 200602