Thermodynamics of Precision in Markovian Open Quantum Dynamics

TL;DR

This paper explores the quantum analogs of thermodynamic uncertainty relations in Markovian open quantum systems, revealing how quantum coherence influences the trade-offs between fluctuations and thermodynamic quantities.

Contribution

It derives finite-time bounds on fluctuations in quantum jump processes, highlighting the role of quantum coherence in these uncertainty relations.

Findings

Quantum coherence enhances the product of fluctuation and entropy production.

Classical uncertainty relations partially survive in quantum regimes.

Bounds apply to arbitrary initial states in open quantum systems.

Abstract

The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this paper, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.