Inequality for von Neumann entropy change under measurement and dissipation

TL;DR

This paper establishes a fundamental lower bound on the average von Neumann entropy change in quantum systems under measurement and dissipation, highlighting quantum-specific contributions and generalizing classical thermodynamic inequalities.

Contribution

It introduces a universal inequality that bounds entropy change, incorporating quantum effects like coherence disturbance and measurement backaction, extending classical relations to quantum systems.

Findings

Derived a lower bound on entropy change in quantum systems.

Identified quantum-specific contributions to entropy production.

Generalized classical thermodynamic inequalities to the quantum domain.

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.