Einstein Boxes and EPR as Thermodynamic Cycles: A Preparation-Frame Taxonomy of the Wave Function

Einstein's boxes and the Einstein–Podolsky–Rosen (EPR) correlations are examined as thermodynamic protocols with explicit preparation, access, and restoration requirements. For a finite rectangular partition we derive implicit analytic spectral equations, insertion-work expressions, and leading finite-time excitation corrections. For an exactly centered barrier, reflection symmetry separates the even and odd sectors, so closure of the lowest doublet gap alone does not invalidate symmetric adiabatic splitting. Small offsets remove this selection rule; we quantify the resulting transition amplitude and its dependence on the pointer position variance. Treating the partition apparatus quantum mechanically distinguishes accessible records from globally retained coherence: partial tracing yields an improper mixture and does not establish a classical ontology. For EPR we compare three measurement patterns and distinguish ideal register reset from complete-cycle restoration. A globally controlled pure Bell state and a classically correlated mixed pair with the same computational-basis statistics exhibit a one-bit ideal reset-heat differential. This differential quantifies global purity under specified access conditions, not a universal entanglement advantage: retained classical seeds, measurement records, transport, communication, and control restoration belong in a parity-matched ledger. A two-axis preparation–access taxonomy then organizes the Einstein, Bohr, Everett, and Pusey–Barrett–Rudolph discussions without identifying thermodynamic cost with ontic support. The result is a resource-explicit connection between foundational description and thermodynamic operation, with experimentally relevant requirements for testing the conditional purity comparison.