Physically constrained quantum clock-driven dynamics

TL;DR

This paper develops a realistic framework for quantum clocks in thermal machines, analyzing how clock imperfections affect system control and establishing fundamental limits based on energy-time uncertainty relations.

Contribution

It introduces a physically consistent model of quantum clock dynamics that accounts for realistic imperfections and derives bounds on clock degradation using a generalized uncertainty principle.

Findings

Derived a lower bound on clock degradation due to imperfections.

Established trade-offs between clock accuracy and energy uncertainty.

Provided a simplified, physically consistent description of quantum clock dynamics.

Abstract

Thermal machines are physical systems designed to convert thermal energy into practical work through cyclic state transformations. A key component in such a machine is a clock-equipped control element that dictates which interaction Hamiltonian governs the system-reservoir interactions at specific times, while itself remaining unaffected. However, in the context of quantum dynamics, it is well known that maintaining perfect isolation is practically impossible, except under highly idealized conditions. In this study, we begin with such an idealized model for a clock and systematically relax its main assumptions to develop a more realistic framework. Our approach yields a simplified yet physically consistent description of clock dynamics, enabling the analysis of deviations from ideal time-keeping, which we interpret as clock degradation. We introduce a continuous time operator to derive a lower bound on this degradation, grounded in a generalized time-energy uncertainty relation. These results highlight trade-offs between clock performance and energy uncertainty in physically realizable control schemes.