Energy backflow and non-Markovian dynamics

TL;DR

This paper investigates the relationship between energy backflow and non-Markovian dynamics in quantum systems, using full counting statistics to quantify energy exchange and identifying conditions where energy backflow correlates with non-Markovianity.

Contribution

It introduces a quantifier for energy backflow linked to non-Markovianity and applies it to the spin-boson model within a second order approximation.

Findings

Energy backflow occurs in non-Markovian regimes.

A quantifier effectively captures energy backflow.

Parameter regions with higher energy backflow are identified.

Abstract

We explore the behavior in time of the energy exchange between a system of interest and its environment, together with its relationship to the non-Markovianity of the system dynamics. In order to evaluate the energy exchange we rely on the full counting statistics formalism, which we use to evaluate the first moment of its probability distribution. We focus in particular on the energy backflow from environment to system, to which we associate a suitable condition and quantifier, which enables us to draw a connection with a recently introduced notion of non-Markovianity based on information backflow. This quantifier is then studied in detail in the case of the spin-boson model, described within a second order time-convolutionless approximation, observing that non-Markovianity allows for the observation of energy backflow. This analysis allows us to identify the parameters region in which energy backflow is higher.