Quantum Work Statistics with Initial Coherence.

María Díaz,Mauro Paternostro,Giacomo Guarnieri

doi:10.3390/e22111223

María Díaz, Mauro Paternostro + Show 1 more

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https://doi.org/10.3390/e22111223

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Abstract

The two-point measurement scheme for computing the thermodynamic work performed on a system requires it to be initially in equilibrium. The Margenau–Hill scheme, among others, extends the previous approach to allow for a non-equilibrium initial state. We establish a quantitative comparison between both schemes in terms of the amount of coherence present in the initial state of the system, as quantified by the -coherence measure. We show that the difference between the two first moments of work, the variances of work, and the average entropy production obtained in both schemes can be cast in terms of such initial coherence. Moreover, we prove that the average entropy production can take negative values in the Margenau–Hill framework.

Highlights

In the quest for the understanding of the interplay between thermal and quantum fluctuations that determine the energy exchange processes occurring at the nano- and micro-scale, the identification of the role played by quantum coherences is paramount [1,2]
Owing to the success that it has encountered in classical stochastic thermodynamics, the current approach to the determination of the statistics of such energetics in the quantum domain is based on the so-called two-point measurement (TPM) protocol [13,14,15]: the energy change of a system driven by a time-dependent protocol is measured both at the initial and final time of the dynamics
It is crucial to pinpoint the role that the quantum coherences either present in the initial state of the system or created throughout its dynamics have in the setting up of the MH phenomenology. This is precisely the point addressed in this paper, where we thoroughly investigate the differences between the statistics entailed by the TPM and MH approaches and relate them to the value taken by well-established quantifiers of quantum coherence [31] over the initial state of the system, as well as dynamical features of the process that the latter undergoes

Summary

Introduction

In the quest for the understanding of the interplay between thermal and quantum fluctuations that determine the energy exchange processes occurring at the nano- and micro-scale, the identification of the role played by quantum coherences is paramount [1,2]. The application of the TPM protocol has led to the possibility to address the statistics of quantum energy fluctuations in a few interesting experiments [16,17,18,19,20] Such a strategy has a considerable drawback in that, by performing a strong initial projective measurement, all quantum coherences in the energy eigenbasis are removed, de facto washing out the possibility of quantum interference to take place. This fundamental bottleneck has led to efforts aimed at formulating coherence-preserving protocols for the quantification of the statistics of energy fluctuations resulting from a quantum process [21,22,23,24].

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