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arXiv · 2512.12862

A no-go theorem for irreversibility along single-branch collapse dynamics

A. Della Corte·L. Guglielmi·M. Farotti
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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.

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A. Della Corte, L. Guglielmi, M. Farotti. 2025-12-14. A no-go theorem for irreversibility along single-branch collapse dynamics. https://arxiv.org/abs/2512.12862

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