🤖 AI Summary
This work establishes a universal fluctuation and precision-bound theory for entropy production (EP) in nonequilibrium thermodynamics of stochastic systems with multivariate interactions represented by Bayesian networks. Methodologically, it introduces, for the first time, conditional fluctuation theorems and the thermodynamic uncertainty relation (TUR) into the Bayesian network thermodynamics framework, integrating stochastic processes, information geometry, and large-deviation analysis to derive exact fluctuation theorems for EP of arbitrary subsystem collections—and their conditional EP—and to formulate a novel TUR linking global EP to the precision of probability currents across constituent systems. Key contributions are: (1) quantitative characterization of how directed causal structure constrains thermodynamic precision limits; (2) derivation of a family of universal fluctuation theorems and structure-dependent TURs; and (3) provision of a scalable theoretical foundation for cooperative thermodynamic control in multi-agent systems.
📝 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.