Thermodynamic inference of correlations in nonequilibrium collective dynamics

The theory of stochastic thermodynamics has revealed many useful fluctuation relations, with the thermodynamic uncertainty relation (TUR) being a theorem of major interest. When many nonequilibrium currents interact with each other, a naive application of the TUR to an individual current can result in an apparent violation of the TUR bound. Here, we explore how such an apparent violation can be used to put a lower bound on the strength of correlations $C$ as well as the number $N$ of interacting currents in collective dynamics. This lower bound is a combined bound on $C(N-1)$ if only one current is measured, or a bound on $N$ if two currents are measured. Our proposed protocol allows for the inference of hidden correlations in experiment, for example when a team of molecular motors pulls on the same cargo but only one or a subset of them is fluorescently tagged. By solving analytically and numerically several models of many-body nonequilibrium dynamics, we ascertain under which conditions this strategy can be applied and the inferred bound on correlations becomes tight.