A no-go theorem for irreversibility along single-branch collapse dynamics
Abstract
We study finite dimensional quantum systems with arbitrary collapse events, establishing, under no-information-erasure conditions, a structural no-go for operational irreversibility along single branches of the collapse dynamics. More precisely, we prove that, for every physically admissible selector of the collapse dynamics, there exists a topologically closed, forward-invariant subset of the projective state space on which any two states can be connected with arbitrarily fine Fubini-Study precision and arbitrarily small integrated energetic cost. This shows that the preservation of information along a realized branch of outcomes guarantees islands of quasi-reversibility, while genuine irreversibility requires additional ingredients such as non-compactness or information erasure. KEYWORDS: Quantum collapse dynamics; Quasi-reversibility; Chain-recurrence; Information non-erasure.
Cite
@article{arxiv.2512.12862,
title = {A no-go theorem for irreversibility along single-branch collapse dynamics},
author = {A. Della Corte and L. Guglielmi and M. Farotti},
journal= {arXiv preprint arXiv:2512.12862},
year = {2026}
}