Thermodynamic Irreversibility from Inaccessible Endogenous Quantum Histories

Abstract: Microscopic unitary dynamics preserves all fine information, yet an isolated finite system can show a robust thermodynamic window in which the entropy associated with a restricted record rises. We ask why information hidden from the current record usually fails to rebuild a low-entropy macrostate. For a fixed projective record, every finite step separates exactly into the evolution predicted from the record alone and an exact correction carried by unresolved microscopic structure. The record-only contribution starts only at second order in time, so all instantaneous change of the record comes from hidden currents between macrostates. We derive the exact entropy rate, separate entropy-spreading from return-oriented currents, and resolve those currents into energy-gap amplitudes. Transitions with the same gap add coherently, revealing how the Hamiltonian and the microscopic state organize hidden information for return. In interacting mixing dynamics the current power is spread over many frequencies; free and deliberately commensurate controls progressively concentrate it, and the engineered dynamics reconstructs a low-entropy macrostate. An independent distribution-level test separates hidden dynamical activity from finite-step return, and an exact classical measure-preserving counterpart shows which parts of the construction are not uniquely quantum. Within the specified record and observation window, irreversibility is therefore not loss of microscopic information, but the failure of that information to organize currents that restore macroscopic order.