The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system

TL;DR

This paper investigates why the thermodynamic uncertainty relation bounds are looser in open quantum systems, revealing that quantum coherence's imaginary part loosens the bound while the real part tightens it.

Contribution

It identifies the specific role of quantum coherence components in influencing the tightness of TUR bounds in open quantum systems.

Findings

Imaginary part of quantum coherence loosens the TUR bound.

Real part of quantum coherence tightens the TUR bound.

Quantum coherence affects dissipation and fluctuations in quantum systems.

Abstract

The thermodynamic uncertainty relations (TURs), originally discovered for classical systems, dictate the trade-off between dissipation and fluctuations of irreversible current, specifying a minimal bound that constrains the two quantities. In a series of effort to extend the relation to the one under more generalized conditions, it has been noticed that the bound is less tight in open quantum processes. To study the origin of the loose bounds, we consider an external field-driven transition dynamics of two-level quantum system weakly coupled to the bosonic bath as a model of open quantum system. The model makes it explicit that the imaginary part of quantum coherence, which contributes to dissipation to the environment, is responsible for loosening the TUR bound by suppressing the relative fluctuations in the irreversible current of transitions, whereas the real part of the coherence tightens it. Our study offers a better understanding of how quantum nature affects the TUR bound.