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Thermodynamic uncertainty relations (TURs) are general lower bounds on thesize of fluctutations of dynamical observables. They have importantconsequences, one being that the precision of estimation of a current islimited by the amount of entropy production. Here we prove the existence ofgeneral upper bounds on the size of fluctuations of any linear combination offluxes (including all time-integrated currents or dynamical activities) forcontinuous-time Markov chains. We obtain these general relations by means ofconcentration bound techniques. These ``inverse TURs'' are valid for all timesand not only in the long time limit. We illustrate our analytical results witha simple model, and discuss wider implications of these new relations.

Inverse thermodynamic uncertainty relations: general upper bounds on the fluctuations of trajectory observables