Nonequilibrium fluctuation-response relations for state observables

Time-integrated state observables, which quantify the fraction of time spent by the system in a specific pool of states, are important in many fields, such as chemical sensing or the theory of fluorescence spectroscopy. We derive exact identities, called Fluctuation-Response Relations (FRRs), that connect the fluctuations of such observables to their response to external perturbations in nonequilibrium steady state of Markov jump processes. Using these results, we derive a first known upper bound on fluctuations of state observables, as well as some new lower bounds. We further demonstrate how our identities provide a deeper understanding of the mechanistic origin of fluctuations and reveal their properties dependent only on system topology, which may be relevant for model inference using measured data.