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arXiv · 2605.08652

Quantum Relative Entropy and the Mean-Field Limit

Gaoyue Guo·Hao Liang·Zhenfu Wang
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Abstract

We develop a quantum relative entropy method for the mean-field limit of quantum many-body systems. For closed systems governed by the von Neumann equation, we prove a quantitative stability estimate between the $N$-body density matrix and the tensorized solution of the Hartree equation. The argument is based on an entropy production identity, a cancellation mechanism for the centered two-body fluctuation, and a combinatorial estimate controlling the remaining mixed moments. As a consequence, we obtain propagation of chaos in trace norm for fixed marginals. We further combine the entropy estimate with known semiclassical Wasserstein bounds to derive a convergence estimate that is uniform in the Planck constant in an appropriate joint mean-field and semiclassical regime. Finally, we extend the method to finite-dimensional open quantum systems governed by Lindblad dynamics. In this setting, we establish an analogous relative entropy estimate for general bounded two-body interactions, where the mean-field potential is defined through partial trace. This shows that the entropy method does not rely on any special tensor-product decomposition of the interaction.

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Gaoyue Guo, Hao Liang, Zhenfu Wang. 2026-05-09. Quantum Relative Entropy and the Mean-Field Limit. https://arxiv.org/abs/2605.08652

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