CSH Talk by David Wolpert: “Uncertainty relations and fluctuation theorems for Bayes nets”

If you are interested in participating, please email to office@csh.ac.at.

Abstract:

The pioneering paper “Information Thermodynamics on Causal Networks” by Sosuke Ito and Takahiro Sagawa (2013) analyzed the non-equilibrium statistical physics of a set of multiple interacting systems, S, whose joint discrete-time evolution is specified by a Bayesian network. The major result of Ito and Sagawa was an integral fluctuation theorem (IFT) governing the sum of two quantities: the entropy production (EP) of an arbitrary single one of the systems, v in the set S, and the transfer entropy from v to the other systems.

Here I extend the analysis in Ito and Sagawa’s paper. I derive several detailed fluctuation theorems (DFTs), concerning arbitrary subsets of all the systems (including the full set). I also derive several associated IFTs, concerning an arbitrary subset of the systems, thereby extending Ito/Sagawa’s IFT. In addition, I derive “conditional” DFTs and IFTs, involving conditional probability distributions rather than—as in conventional fluctuation theorems—unconditioned distributions. I then derive thermodynamic uncertainty relations relating the total EP of the Bayes net to the set of all the precisions of probability currents within the individual systems.