Exact solution to quantum dynamical activity

Abstract

The quantum dynamical activity constitutes a thermodynamic cost in trade-off relations such as the quantum speed limit and the quantum thermodynamic uncertainty relation. However, calculating the quantum dynamical activity has been a challenge. In this paper, we present the exact solution for the quantum dynamical activity by deploying the continuous matrix product state method. Moreover, using the derived exact solution, we determine the upper bound of the dynamical activity, which comprises the standard deviation of the system Hamiltonian and jump operators. We confirm the exact solution and the upper bound by performing numerical simulations.

16 pages, 1 figure

References in corpus (5)

• Thermodynamic uncertainty relation for biomolecular processes
• Continuous Matrix Product States for Quantum Fields
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state
• Holographic quantum states

Cited by in corpus (7)

• Time-resolved Stochastic Dynamics of Quantum Thermal Machines
• Thermodynamic concentration inequalities and tradeoff relations
• Deterministic Equations for Feedback Control of Open Quantum Systems III: Full counting statistics for jump-based feedback
• A unified framework of unitarily residual measures for quantifying dissipation
• Fundamental precision limits in finite-dimensional quantum thermal machines
• Framework for fluctuating times and counting observables in stochastic excursions
• Counting observables in stochastic excursions