Work Measurement in OPEN Quantum System.

Youyang Xu

doi:10.3390/e24020180

Abstract

Work is an important quantity in thermodynamics. In a closed quanutm system, the two-point energy measurements can be applied to measure the work but cannot be utilized in an open quantum system. With the two-point energy measurements, it has been shown that the work fluctuation satisfies the Jarzynski equality. We propose a scheme to measure the work in an open quantum system through the technique of reservoir engineering. Based on this scheme, we show that the work fluctuation in open quantum system may violate the Jarzynski equality. We apply our scheme to a two-level atom coupled to an engineered reservoir and numerically justify the general results, especially demonstrating that the second law of thermodynamics can be violated.

Highlights

Based on this scheme, we obtain a fluctuation theorem of the work and show that it is different from the Jarzynski equality
We show how to obtain the work fluctuation theorem in an open quantum system
Work is an important quantity in thermodynamics, but it could not be measured directly in a open quantum system before

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. W = ∆U = Trρ f H f − Trρi H i , with the superscript f and i representing the final and initial times of the process, respectively This method has been applied to demonstrate many important conclusions in quantum thermodynamics, such as to study the fluctuation relations of the work of quantum driven system [18], it can only be used in the case of a closed system. These two problems result in the Jarzynski equality of open quantum systems being unable to be explored experimentally We note that both the above problems originate from the interaction with the heat reservoir. We will propose a scheme to measure the work of an open quantum system through reservoir engineering Based on this scheme, we obtain a fluctuation theorem of the work and show that it is different from the Jarzynski equality. The experimental feasibility based on a single trapped ion is provided and shows that the second law of thermodynamics presented by W ≥ ∆F can be violated

Work Measurement of an Open Quantum System

Work Fluctuation Theorem of Open Quantum System

Experimental Feasibility

Conclusions