Thermodynamic Uncertainty Relations for Multipartite Processes

The thermodynamic uncertainty relations (TURs) provide upper bounds on the precision of an arbitrary current in a non-equilibrium system in terms of the entropy production of that system. All TURs derived so far have concerned single physical systems. However, many physical scenarios of interest involve multiple interacting systems, e.g. organelles within a biological cell. Here we show how to extend the previously derived TURs to those scenarios by exploiting a recently introduced framework of the thermodynamics of interacting systems [arXiv: 2003.11144]. These extended TURs bound the global EP over a set of interacting systems in terms of a weighted sum of the precisions of local currents emerging within those systems - plus an information-theoretic correction term. This information-theoretic correction term is a generalization of the multi-information among the states of the overall system. We also obtain expressions concerning the relations between the local EPs of the individual systems and the statistical coupling among the currents within these systems. In particular, we derive such results for both the cases of scalar-valued and vector-valued currents within each system. We illustrate our results with numerical experiments.