R. Hamazki Seminar: On rapid quantum thermodynamic processes - from optimal work extraction to thermodynamic uncertainty relation

Although time plays no explicit role in conventional equilibrium thermodynamics, finite-time thermodynamic processes are of fundamental importance. In this talk, I discuss universal principles that govern rapid thermodynamic processes in quantum systems, focusing on (I) optimal work extraction in finite-time closed quantum dynamics [1] and (II) the quasiprobability thermodynamic uncertainty relation [2]. In the first part (I), I present two general results concerning finite-time optimal work extraction problem, where we control energy by unitary time operation generated by a bounded Hamiltonian. The first result establishes a trade-off relation between work and power, two crucial performance metrics for quantum thermodynamic processes. This implies that a rapid protocol is necessary to achieve high power, thereby justifying the importance of our finite-time framework. The second result applies under a new framework, where the set of control operations forms a Lie algebra. In this case, we discover that the optimal protocol is remarkably simple: one can use a time-independent Hamiltonian determined by a closed nonlinear equation. We verify our results in concrete setups involving both few-level and many-body systems. In the second part (II), I present a new quantum extension of thermodynamic uncertainty relations (TUR), which relates the dissipation, current, and dynamical fluctuations. While dynamical fluctuations are quantified by the joint probability distribution of two-point measurement outcomes in classical systems, their extension to quantum systems are not straightforward, since the two-point measurement scheme destroys initial quantum coherence in quantum systems. Here, we overcome this problem by employing the Terletsky–Margenau–Hill quasiprobability and derive the TUR free from the backaction problem. As an application of the quasiprobability TUR, we also mention a new criterion for the dissipationless heat current, which has been recently proposed as a demonstration of quantum advantage. [1] S. Sugimoto, T. Sagawa, and R. Hamazaki, arXiv:2508.20512 (2025) [2] K. Yoshimura and R. Hamazaki, arXiv: 2508.14354 (2025)