Finite Measured Entropy Production Does Not Imply Finite Microscopic Irreversibility

arXiv:2611.13110v1 Announce Type: new Abstract: Coarse-grained measurements provide a lower bound on entropy production, but how much microscopic irreversibility can they conceal? We construct a driven quantum system in which an imperfect counter registers a finite, strictly positive arrow of time while the microscopic entropy production is infinite. The system is a degenerate parametric oscillator below threshold, coupled to a thermal reservoir through repeated interactions with bosonic ancillas. The oscillator sustains a finite, positive heat current into the vacuum bath, where absorption is forbidden and forward and reverse trajectory laws have different supports.