Reversibility in finite-dimensional collapse dynamics
A. Della Corte, L. Guglielmi, M. Farotti
TL;DR
The paper investigates reversibility in finite-dimensional quantum systems undergoing collapse events by fixing a physically admissible realization map $D$ and analyzing the induced dynamics on the projective state space with topological-dynamics tools. It shows that, even without regularity assumptions on the evolution map, there exists a topologically closed, forward-invariant subsystem where states can be connected with arbitrarily small Fubini–Study distance and arbitrarily small integrated energy cost, i.e., an island of quasi-reversibility. This constitutes a structural no-go for an operational arrow of time along realized branches in the no-erasure regime, and it clarifies that genuine irreversibility requires non-compactness, explicit erasure, or coupling to reservoirs. The work connects to Landauer’s principle and Bennett’s resolution of the Maxwell demon, highlighting that memory and information-retention constraints are essential to generate thermodynamic irreversibility in quantum collapse scenarios, even in finite dimensions.
Abstract
We study finite dimensional quantum systems with arbitrary collapse events, establishing, under no-information-erasure conditions, a structural no-go for trajectory-level operational irreversibility. More precisely, we fix a realization map (a physically admissible selector of the collapse dynamics) and do not rely on any regularity of the induced dynamics. We prove that, for every realization 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 guarantees islands of quasi-reversibility, while genuine irreversibility requires additional ingredients such as non-compactness, explicit erasure, or coupling to reservoirs. KEYWORDS: Quantum collapse dynamics; Quasi-reversibility; Chain-recurrence; Information non-erasure.