This preprint presents an operational formulation and resolution of Loschmidt’s paradox. While microscopic classical and quantum dynamics are formally time-reversible, the paradox implicitly assumes that the inverse evolution is physically implementable by operations available after forward dynamics has redistributed information across degrees of freedom. The work isolates this hidden operational premise and demonstrates that microscopic reversibility does not entail operational reversibility under explicit accessibility constraints. In a classical linearized setting, a bounded-gain control model restricted to accessible degrees of freedom yields a nonzero lower bound on local inversion error whenever information has leaked into inaccessible variables. In a quantum setting, a verifiable reversal task on accessible correlations is introduced, and information leakage into an inaccessible environment enforces a nonzero error floor for any recovery channel acting only on the accessible subsystem. The results show that Loschmidt’s objection is operationally dissolved: the inverse dynamics may exist mathematically while remaining physically unattainable within the admissible operation set. No appeal is made to entropy increase, coarse-graining, probabilistic postulates, or fundamental time asymmetry.
FRANCISCO OYARZUN (Mon,) studied this question.