Thermodynamic Uncertainty Relations for Multipartite Processes

Abstract

The thermodynamic uncertainty relations (TURs) provide lower bounds on the entropy production (EP) of a system in terms of the statistical precision of an arbitrary current in that system. All conventional TURs derived so far have concerned a single physical system, differing from one another in what properties they require the system to have. However, many physical scenarios of interest involve multiple interacting systems, e.g. organelles within a biological cell. Here we show how to extend the conventional 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. Importantly, these extended TURs can bound the global EP even when the global system does not meet any of the requirements of the conventional TURs. After deriving these extended TURs we use them 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.