Unravelling the role of coherence in the first law of quantum thermodynamics

TL;DR

This paper investigates how quantum coherence influences the first law of thermodynamics at the quantum level, revealing a mathematical inconsistency and emphasizing the importance of coherence dynamics for consistency.

Contribution

It identifies a fundamental inconsistency between two quantum formulations of the first law and highlights the role of coherence dynamics in resolving it.

Findings

Existence of a mathematical inconsistency between two quantum first law formulations

The energetic role of coherence dynamics is crucial for consistency

Illustrative examples with two-level systems demonstrate the findings

Abstract

One of the fundamental questions in the emerging field of quantum thermodynamics is the role played by coherence in energetic processes that occur at the quantum level. Here, we address this issue by investigating two different quantum versions of the first law of thermodynamics, derived from the classical definitions of work and heat. By doing so, we find out that there exists a mathematical inconsistency between both scenarios. We further show that the energetic contribution of the dynamics of coherence is the key ingredient to establish the consistency. Some examples involving two-level atomic systems are discussed in order to illustrate our findings.