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Stochastic thermodynamics extends classical thermodynamics to small systemsin contact with one or more heat baths. It can account for the effects ofthermal fluctuations and describe systems far from thermodynamic equilibrium. Abasic assumption is that the expression for Shannon entropy is the appropriatedescription for the entropy of a nonequilibrium system in such a setting. Here,for the first time, we measure experimentally this function. Our system is amicron-scale colloidal particle in water, in a virtual double-well potentialcreated by a feedback trap. We measure the work to erase a fraction of a bit ofinformation and show that it is bounded by the Shannon entropy for a two-statesystem. Further, by measuring directly the reversibility of slow protocols, wecan distinguish unambiguously between protocols that can and cannot reach theexpected thermodynamic bounds.

Direct measurement of nonequilibrium system entropy is consistent with Gibbs-Shannon form