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The thermodynamic uncertainty relation expresses a universal trade-offbetween precision and entropy production, which applies in its originalformulation to current observables in steady-state systems. We generalize thisrelation to periodically time-dependent systems and, relatedly, to a largerclass of inherently time-dependent current observables. In the context of heatengines or molecular machines, our generalization applies not only to the workperformed by constant driving forces, but also to the work performed whilechanging energy levels. The entropic term entering the generalized uncertaintyrelation is the sum of local rates of entropy production, which are modified bya factor that refers to an effective time-independent probability distribution.The conventional form of the thermodynamic uncertainty relation is recoveredfor a time-independently driven steady state and, additionally, in the limit offast driving. We illustrate our results for a simple model of a heat enginewith two energy levels.

A generalization of the thermodynamic uncertainty relation to periodically driven systems