Energy backflow and non-Markovian dynamics

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.Comment: 11 pages, 5 figures; published versio

Heat flux and information backflow in cold environments

“…Even for initial pairs in the driven case, where both information and heat flow back during the propagation, this does not happen simultaneously. While the dynamics is non-Markovian (i.e., there are initial pairs which show information backflow) and there is heat backflow into the system for certain (other) initial preparations as in [39], we do not find any correlations between heat flux and information backflow for the same pair of initial states.…”

Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics

“…From the dynamical control perspective, the timedependent modulation of heat transfer in the NESB model has also attracted tremendous attention, enriching the transfer mechanisms [14][15][16][17][29][30][31][32][33]. The typical realization of the dynamical modulation is the adiabatic quantum pump, which was originally proposed by D. J. Thouless to study the effect of Berry-phase-induced quantization on closed-system transport [34].…”

Energy backflow in strongly coupled non-Markovian continuous-variable systems

“…an energy flow from the reduced system (environment) to the environment (reduced system). In the Born-Markov semigroup limiting case, θ(t) becomes a monotonic function of time, thus indicating a steady energy flow from the higher to the lower temperature system [14,15] that vanishes in the case system and environment start with the same initial temperature. Beyond the Born-Markov description, the energy flow becomes an oscillating function of time, whose behavior can strongly vary depending on the various parameters characterizing the dynamics.…”

“…Building on this condition, a measure for the total amount of energy which has flown back from the environment to the system during the evolution can be introduced as [15] ∆q back = max…”

“…In this work, we consider the energy exchange dynamics in non-driven open CV systems using full counting statistics methods, referring to a recently introduced measure of energy backflow [15], which quantifies the total amount of energy flowing back to the system from the heat bath. In particular, we calculate it for a model of quantum Brownian motion (QBM) both in the weak coupling regime, using an analytic approach, and in the strong coupling regime by employing a numerical strategy based on exact diagonalization of a large but finite heat bath.…”