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Europhysics Letters (EPL)

Finite-time availability in a quantum system

K. H. Hoffmann, Peter Salamon

Published Feb 1, 2015• 8 citations
Publisher

Abstract

Classically, availability refers to the work available in any reversible process that brings about equilibrium between the system and its environment. Here we introduce an additional meaning of availability as the maximum work associated with the change of an external parameter in the Hamiltonian of a quantum system. This availability can be gained in a FEAT process and for times larger than or equal to the FEAT time, there exists an optimal control that achieves the available work. For shorter times, quantum friction effects are unavoidable and the available work is thereby lowered. This finite-time availability is quantified here as a function of the time available.

DOI
10.1209/0295-5075/109/40004

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Classically, availability refers to the work available in any reversible process that brings about equilibrium between the system and its environment. Here we introduce an additional meaning of availability as the maximum work associated with the change of an external parameter in the Hamiltonian of a quantum system. This availability can be gained in a FEAT process and for times larger than or equal to the FEAT time, there exists an optimal control that achieves the available work. For shorter times, quantum friction effects are unavoidable and the available work is thereby lowered. This finite-time availability is quantified here as a function of the time available.
Abstract The availability of a thermodynamic system out of equilibrium with its environment describes its ability to perform work in a reversible process which brings it to equilibrium with this environment. Processes in finite time can usually not be performed reversibly thus leading to unavoidable losses. In order to account for these losses the concept of finite time availability was introduced. We here add a new feature through the introduction of quantum finite time availability for an ensemble of parametric oscillators. For such systems there exists a certain critical time, the FEAT time. Quantum finite time availability quantifies the available work from processes which are shorter than the FEAT time of the oscillator ensemble.
The availability of a thermodynamic system with respect to an environment is the maximum work, which can be gained from bringing it into equilibrium with its environment by a reversible process. If the process has to proceed in finite time, there will be unavoidable losses diminishing the availability; this consequence is captured by the Finite-Time Availability. Here we consider the consequences of an availability extracting process for a paradigmatic quantum system, the parametric harmonic oscillator. Differences and similarities between its Quantum Finite-Time Availability and the classical Finite-Time Availability of an ideal gas in a cylinder with a piston are discussed.
This paper considers the problem of obtaining maximum work from a conservative quantum system corresponding to a given change in an external parameter in the Hamiltonian. The example we present is a non-interacting collection of harmonic oscillators with a shared frequency omega which changes from a given initial to a given final value. The example is interesting for its role in experiments at ultra-low temperatures and for probing finite-time versions of the third law of thermodynamics. It is also the simplest system displaying quantum friction, which represents loss mechanisms in any reversible prelude to a thermal process. The example leads to a new type of availability. It is also the first example of a minimum time for transitions between thermal states of a thermodynamic system.
We demonstrate the effectiveness of quantum optimal control techniques in harnessing irreversibility generated by non-equilibrium processes, implemented in unitarily evolving quantum many-body systems. We address the dynamics of a finite-size quantum Ising model subjected to finite-time transformations, which unavoidably generate irreversibility. We show that work can be generated through such transformation by means of optimal controlled quenches, while quenching the degree of irreversibility to very low values, thus boosting the efficiency of the process and paving the way to a fully controllable non-equilibrium thermodynamics of quantum processes.
Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production.
In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced.