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  • Letter
  • Open Access

Scaling of von Neumann entropy in dissipative Liouvillian dynamics

Wei-Zhu Yi1,2, Hao-Jie Lin1, Ze-Xun Lin3,4,5, Rui Wang2,6,7,*, and Wei-Qiang Chen1,8,†

  • *Contact author: rwang89@nju.edu.cn
  • †Contact author: chenwq@sustech.edu.cn
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Phys. Rev. Research 7, L022032 – Published 7 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022032

Abstract

The universal dynamical phenomenon of von Neumann entropy plays an important role in understanding the nature of open many-body systems, as it uncovers general collective properties driven by correlation and quantum dynamics. Here, we reveal a universal time evolution behavior of bipartite von Neumann entropy in open quantum systems with dissipation into the surrounding environments. The coupling with the environment leads to a rapid growth of the entropy, resulting in an exotic short-time evolution law, S(t)∼−tlnt. Such a fast growth behavior is proved to be a general phenomenon for generic many-body systems in dissipative environments, as long as the systems exhibit well-defined fermionic quasiparticles. Interestingly, even for strongly interacting Luttinger liquids, which display vanishing fermionic but emergent bosonic quasiparticles, the same dynamical phenomenon is still found to persist. These results demonstrate a universal Liouvillian dynamical feature that has no counterpart in isolated Hamiltonian systems.

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Phys. Rev. Research 7, L022032– Published 7 May, 2025
  • Received 15 April 2024
  • Accepted 21 April 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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