Optimal Work Extraction from Finite-Time Closed Quantum Dynamics

• URL: http://arxiv.org/abs/2508.20512v2
• Date: Tue, 14 Oct 2025 17:53:32 GMT
• Title: Optimal Work Extraction from Finite-Time Closed Quantum Dynamics
• Authors: Shoki Sugimoto, Takahiro Sagawa, Ryusuke Hamazaki,
• Abstract summary: We investigate the problem of finite-time optimal work extraction from closed quantum systems.<n>We introduce a general framework based on Lie algebras to reduce the optimal work extraction problem to an analytically or numerically efficiently tractable form.<n>Our results highlight the necessity of rapid protocols to achieve the maximum power.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Extracting useful work from quantum systems is a fundamental problem in quantum thermodynamics. In scenarios where rapid protocols are desired -- whether due to practical constraints or deliberate design choices -- a fundamental trade-off between power and efficiency is yet to be established. Here, we investigate the problem of finite-time optimal work extraction from closed quantum systems, subject to a constraint on the magnitude of the control Hamiltonian. We first reveal the trade-off relation between power and work under a general setup, stating that these fundamental performance metrics cannot be maximized simultaneously. We then introduce a general framework based on Lie algebras, which involves a wide range of control problems such as many-body control of the Heisenberg model and the SU(n)-Hubbard model. This framework enables us to reduce the optimal work extraction problem to an analytically or numerically efficiently tractable form. The resulting optimal protocol turns out to be remarkably simple: it suffices to use a time-independent control Hamiltonian in the interaction picture, determined by a nonlinear self-consistent equation. By exploiting the Lie-algebraic structure of the controllable terms, our approach is applicable to quantum many-body systems with an efficient numerical computation. Our results highlight the necessity of rapid protocols to achieve the maximum power and establish a theoretical framework for designing optimal work extraction protocols under realistic time constraints.

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