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  • Open Access

Thermodynamic speed limits in isolated quantum systems

Rikuya Kobashi*

  • *Contact author: kobashi.rikuya.84s@st.kyoto-u.ac.jp
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Phys. Rev. Research 8, 043140 – Published 9 November, 2026

DOI: https://doi.org/10.1103/k16k-nx74

Abstract

We derive thermodynamic speed limits for isolated quantum systems undergoing finite-time unitary driving. The key ingredient is a set of generalized second-law inequalities: For the Gibbs entropy and for several thermodynamically motivated observational entropies, the entropy production is bounded from below by a function of the Vu-Saito quantum Wasserstein distance between the initial and final coarse-grained states. These inequalities yield lower bounds on the operation time in terms of the average entropy-production rate. We apply the framework to system-bath coarse graining, local-energy coarse graining, and diagonal entropy, and illustrate the resulting bounds with numerical and analytically solvable examples. Our results provide a thermodynamic characterization of finite-time state transformations in isolated quantum systems and clarify how coarse-grained entropy production constrains macroscopic reachability.

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Phys. Rev. Research 8, 043140– Published 9 November, 2026
  • Received 18 February 2026
  • Accepted 6 October 2026
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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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