Thermodynamic Uncertainty of Work in Time-Dependently Driven Open Quantum Systems
Abstract
We derive a thermodynamic uncertainty relation for work in an open quantum system driven by a time-dependent protocol and subject to repeated projective energy measurements. The protocol is represented by a sequence of protocol quenches separated by finite-time Lindblad evolution, so that work is accumulated at the quenches while dissipation occurs between them. The resulting work statistics obey the Gallavotti-Cohen symmetry to give rise to the Crooks and Jarzynski fluctuation relations. By perturbing the dissipative dynamics and combining the Cramér--Rao inequality with the quantum Fisher information, we obtain Var W/[τ∂τ⟨ W⟩]2≥ 1/F≥max(1/A,2/E), where ⟨ W⟩ is the work expectation value, Var W is the variance of work, F is the Fisher information, A is the dynamical activity, E is the dimensionless entropy production, and τ is the switching time interval between quenches. The two thermodynamic bounds follow from two independent perturbations that generate the same response of the work statistics. We illustrate the relation for a dissipative two-level system under square-wave and sinusoidal driving and show that the tighter thermodynamic bound can depend on the driving protocol and switching time scale.
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BibTeX
@misc{kwon2026thermodynamic,
title = {{Thermodynamic Uncertainty of Work in Time-Dependently Driven Open Quantum Systems}},
author = {Chulan Kwon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17032},
eprint = {2609.17032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17032},
}
RIS
TY - UNPB
TI - Thermodynamic Uncertainty of Work in Time-Dependently Driven Open Quantum Systems
AU - Chulan Kwon
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.17032
UR - https://arxiv.org/abs/2609.17032
AB - We derive a thermodynamic uncertainty relation for work in an open quantum system driven by a time-dependent protocol and subject to repeated projective energy measurements. The protocol is represented by a sequence of protocol quenches separated by finite-time Lindblad evolution, so that work is accumulated at the quenches while dissipation occurs between them. The resulting work statistics obey the Gallavotti-Cohen symmetry to give rise to the Crooks and Jarzynski fluctuation relations. By perturbing the dissipative dynamics and combining the Cramér--Rao inequality with the quantum Fisher information, we obtain Var W/[τ∂_τ⟨ W⟩]^2≥ 1/F≥max(1/A,2/E), where ⟨ W⟩ is the work expectation value, Var W is the variance of work, F is the Fisher information, A is the dynamical activity, E is the dimensionless entropy production, and τ is the switching time interval between quenches. The two thermodynamic bounds follow from two independent perturbations that generate the same response of the work statistics. We illustrate the relation for a dissipative two-level system under square-wave and sinusoidal driving and show that the tighter thermodynamic bound can depend on the driving protocol and switching time scale.
ER -