Andreas Dechant, Shin-ichi Sasa

We discuss how to use correlations between different physical observables to improve recently obtained thermodynamics bounds, notably the fluctuation-response inequality and the thermodynamic uncertainty relation (TUR). We show that increasing the number of measured observables will always produce a tighter bound. This tighter bound becomes particularly useful if one of the observables is a conserved quantity, whose expectation is invariant under a given perturbation of the system. For the case of the TUR, we show that this applies to any function of the state of the system. The resulting correlation TUR takes into account the correlations between a current and a noncurrent observable, thereby tightening the TUR. We demonstrate our finding on a model of the ${\mathrm{F}}_{1}$-ATPase molecular motor, a Markov jump model consisting of two rings and transport through a two-dimensional channel. We find that the correlation TUR is significantly tighter than the TUR and can be close to an equality even far from equilibrium.