Abstract We consider the problem of estimating mean entropy production rate in a nonequilibrium process from measurements first-passage quantities associated with single current. For processes large thresholds, references (Roldán et al 2015 Phys. Rev. Lett. 115 250602; Neri 2022 SciPost 12 139) identified ratio observables—involving time, splitting probability, and thresholds—that lower bounds ...