Battery Charging in Collision Models with Bayesian Risk Strategies.

Gabriel T Landi

doi:10.3390/e23121627

Abstract

We constructed a collision model where measurements in the system, together with a Bayesian decision rule, are used to classify the incoming ancillas as having either high or low ergotropy (maximum extractable work). The former are allowed to leave, while the latter are redirected for further processing, aimed at increasing their ergotropy further. The ancillas play the role of a quantum battery, and the collision model, therefore, implements a Maxwell demon. To make the process autonomous and with a well-defined limit cycle, the information collected by the demon is reset after each collision by means of a cold heat bath.

Highlights

In the collision model literature, one assumes that the ancillas are in mixed states
Before discussing an actual implementation, we must first discuss the type of rationale that will be used by the demon in deciding whether the ergotropy is high or low
For comparison, the ergotropy that would be obtained if all ancillas were to be processed by the engine, irrespective of the measurement outcomes

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. First studied in the seminal paper by Rau [1], have seen a revival of interest in recent years [2,3,4] They replace the complex system-bath dynamics by a series of sequential collisions between a system of interest and a continuous stream of small units, called ancillas. High ergotropy ancillas (defined according to some threshold) are allowed to leave, while low ergotropy ones are flagged for further processing That is, they are redirected to go through another quantum channel aimed at increasing their ergotropy further (Figure 1). There is a fundamental cost in erasing the information [61,62], given by Landauer’s principle [63] We model this by assuming that the system is coupled to a cold heat bath that acts for a finite time in between collisions. Decision Theory, to decide whether or not the ancillas should be further processed or not, with the goal of increasing their ergotropy even further

Basic Model

Bayesian Risk Analysis

Qubit–Qubit Model

Results

Energetics

Discussion