Informational Work Storage in Quantum Thermodynamics

Shang-Yung Wang

doi:10.3390/quantum1010005

Abstract

We present a critical examination of the difficulties with the quantum versions of a lifted weight that are widely used as work storage systems in quantum thermodynamics. To overcome those difficulties, we turn to the strong connections between information and thermodynamics illuminated by Szilard’s engine and Landauer’s principle, and consider the concept of informational work storage. This concept is in sharp contrast with the usual one of mechanical work storage underlying the idealization of a quantum weight. An informational work storage system based on maximally mixed qubits that does not act as an entropy sink and is capable of truly distinguishing work from heat is studied. Applying it to the problem of single-shot work extraction in various extraction schemes, we show that for a given system state the maximum extractable work is independent of extraction scheme, in accordance with the second law of thermodynamics.

Highlights

The strong connections between information and thermodynamics, first conceived by Maxwell [1,2,3] and later quantified by Szilard [4], Shannon [5], and Landauer [6], have continued to provide deep insights into the interplay between information theory and thermodynamics of quantum systems [7,8]
An informational work storage system based on maximally mixed qubits, capable of truly distinguishing work from heat, and well suited to thermal operations is studied and applied to the problem of single-shot work extraction [15,18,20,28,29] in various extraction schemes
It is clear that E = τS, where τS is the thermal state of Quantum Rep. 2019, 1 the system associated with HS at temperature T

Summary

Introduction

The strong connections between information and thermodynamics, first conceived by Maxwell [1,2,3] and later quantified by Szilard [4], Shannon [5], and Landauer [6], have continued to provide deep insights into the interplay between information theory and thermodynamics of quantum systems [7,8]. [18], and there is no violation of the second law It has been shown [20] that the origin of the inconsistency is that, when the extracted work is allowed to fluctuate, the quantum weight does not truly distinguish between the work extracted to it from the system and the heat transferred to it from the heat bath. This in turn calls into question the naive notion that work in quantum thermodynamics can be reliably quantified as the change in the energy of a quantum weight. We are able to resolve an inconsistency in the literature with regard to the maximum extractable work in different single-shot extraction schemes

The Framework

Difficulties with the Weight

Informational Work Storage

Application to Single-Shot Work Extraction

Conclusions