Inequality for von Neumann entropy change under measurement and dissipation

Kohei Kobayashi

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arXiv · 2506.12603

Inequality for von Neumann entropy change under measurement and dissipation

Kohei Kobayashi

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Abstract

We derive a universal inequality that provides a lower bound on the ensemble-averaged von Neumann entropy change in a quantum system subject to continuous measurement and dissipation. Our result clarifies how entropy production is fundamentally constrained by three distinct contributions: (i) the non-Hermitian structure of the dissipation operator, (ii) the standard variance associated with measurement-induced fluctuations, and (iii) a generalized quantum variance reflecting the noncommutativity between the measurement observable and the quantum state. This third term vanishes when the state and observable commute, and thus represents a purely quantum contribution arising from coherence disturbance and measurement backaction. The derived inequality generalizes classical information-thermodynamic relations, such as the Sagawa--Ueda inequality, to the quantum regime, providing a new perspective on the trade-offs between information acquisition, control, and entropy production in continuously monitored open quantum systems.

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Kohei Kobayashi. 2025-06-14. Inequality for von Neumann entropy change under measurement and dissipation. https://arxiv.org/abs/2506.12603

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