Thermodynamic Uncertainty Relations for Multipartite Processes.

The thermodynamic uncertainty relations (TURs) provide upper bounds on the precision of an arbitrary current in a system in terms of the entropy production (EP) of that system. All TURs derived so far have concerned a single physical system, varying in the assumptions they make about the dynamics of that system. 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. A common feature of these extended versions of the TURs is that they bound the global EP, jointly generated by the set of interacting systems, in terms of a weighted sum of the precisions of the local currents generated within those systems - plus an information-theoretic correction term. We also exploit these extended TURs to obtain bounds that do not involve the global EP, but instead relate the local EPs of the individual systems and the statistical coupling among the currents generated within those systems. We derive such bounds for both scalar-valued and vector-valued currents within each system. We illustrate our results with numerical experiments.