Class of quasiprobability distributions of work and initial quantum coherence

TL;DR

This paper introduces a class of quasiprobability distributions to describe work in quantum systems with initial coherence, unifying different measurement schemes and revealing the role of coherence in thermodynamic fluctuations.

Contribution

It proposes a new framework for quasiprobability distributions of work that accounts for initial quantum coherence and derives related fluctuation theorems.

Findings

The distributions reduce to standard schemes for incoherent states.

A fluctuation theorem involving quantum coherence is established.

Negativity of the quasiprobability indicates quantum effects.

Abstract

The work is a concept of fundamental importance in thermodynamics. An open question is how to describe the work fluctuation for quantum coherent processes in the presence of initial quantum coherence in the energy basis. With the aim of giving a unified description, here we introduce and study a class of quasiprobability distributions of work, which give an average work equal to the average energy change of the system and reduce to the two-projective measurement scheme for an initial incoherent state. Moreover, we characterize the work with the help of fluctuation relations. In particular, by considering the joint distribution of work and initial quantum coherence, we find a fluctuation theorem involving quantum coherence, from which follows a second law of thermodynamics in the case of initial thermal populations. Furthermore, we propose a way to measure the characteristic function of work and we discuss the negativity of the quasiprobability. The effects of coherence are also investigated for a simple system of a qubit.