Peter Talkner

The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat- and workflows of the machine, the average, the variance of the battery's energy, as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state, its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During the first charging epoch with an engine, the regular measurements speed up the charging, whereas the gain of ergotropy is more pronounced in the absence of measurements. In a later stage, the engine fails to work as such, while it still continues charging the battery that eventually reaches the maximally charged state in the absence of intermediate measurements and a suboptimally charged state for a periodically measured battery. For a refrigerator, the charging of the measured battery also proceeds faster during the first epoch. Only during the second stage, when the machine fails to extract heat from the cold bath, the influence of the measurements becomes less pronounced, leading to rather similar asymptotic states for the two measurement scenarios.

Two approaches are outlined to characterize the fluctuation behavior of work applied to a system by a slow change of a parameter. One approach uses the adiabatic theorems of quantum and classical mechanics, and the other one is based on the behavior of the correlations of the generalized coordinate that is conjugate to the changed parameter. Criteria are obtained under which the work done on small thermally isolated as well as on open systems ceases to fluctuate in a quasistatic process.

Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or heat. For joint work and heat diagnostics, two pointers are needed. These schemes are applied to Otto engines, whose working substance consists of a two-level system. Depending on the engine protocol, the duration of a single cycle may be infinite or finite. Because in the repeated contact scheme, the number of measurements is drastically reduced compared to the repeated measurement scheme, the quantum coherence after and during the contact diagnostics is much better maintained than repeated measurements that destroy any coherence at the end of each stroke. We demonstrate that maximum power, reliability, and efficiency of the engine in the presence of repeated contacts typically outperform these figures of merit of repeated measurements. Due to the improved coherence persistence, heat engines with a finite cycle duration require a larger number of cycles to reach a periodically asymptotic state. Overall, our results document the importance of taking into account the particular nature of diagnostic tools for monitoring and testing purposes but also for feedback control, both in theory and experiment.

Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine’s working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or heat. For joint work and heat diagnostics, two pointers are needed. These schemes are applied to Otto engines, whose working substance consists of a two-level system. Depending on the engine protocol, the duration of a single cycle may be infinite or finite. Because in the repeated contact scheme, the number of measurements is drastically reduced compared to the repeated measurement scheme, the quantum coherence after and during the contact diagnostics is much better maintained than for repeated measurements that destroy any coherence at the end of each stroke. We demonstrate that maximum power, reliability, and efficiency of the engine in the presence of repeated contacts typically outperform these figures of merit of repeated measurements. Due to the improved coherence persistence, heat engines with a finite cycle duration require a larger number of cycles to reach a periodically asymptotic state. Overall, our results document the importance of taking into account the particular nature of diagnostic tools for monitoring and testing purposes but also for feedback control, both in theory and experiment.

In a recent paper [ Phys. Rev. E 101, 050101(R) (2020)] an attempt is presented to formulate the nonequilibrium thermodynamics of an open system in terms of the Hamiltonian of mean force. The purpose of the present comment is to clarify severe restrictions of this approach and to stress that recently noted ambiguities [ Phys. Rev. E 94, 022143 (2016)] of fluctuating thermodynamic potentials cannot be removed in the suggested way.

The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or the reduced phase-space probability density function of a classical open system, the Hamiltonian of mean force not only characterizes the reduced state but also contains full information about the thermodynamics of the considered open system. The resulting thermodynamic potentials all assume the form as the difference of the potentials for the total system and the bare environment in the absence of the system. In contrast to work as a mechanical notion, one faces several problems with the definition of heat which turns out to be largely ambiguous in the case of strong coupling between system and environment. The general theory of the thermodynamics of open systems, in particular, in view of strong coupling, is reviewed and illustrated with several examples. The vagueness of heat is discussed in the context of the ambiguities in the definitions of a fluctuating internal energy and other fluctuating thermodynamic potentials.

The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or the reduced phase-space probability density function of a classical open system, the Hamiltonian of mean force not only characterizes the reduced state but also contains full information about the thermodynamics of the considered open system. The resulting thermodynamic potentials all assume the form as the difference of the potentials for the total system and the bare environment in the absence of the system. In contrast to work as a mechanical notion, one faces several problems with the definition of heat, which turns out to be largely ambiguous in the case of strong coupling between system and environment. The general theory of the thermodynamics of open systems, in particular, in view of strong coupling, is reviewed and illustrated it with several examples. The vagueness of heat is discussed in the context of the ambiguities in the definitions of a fluctuating internal energy and other fluctuating thermodynamic potentials.

A method is proposed that allows one to infer the sum of the values of an observable taken during contacts with a pointer state. Hereby, the state of the pointer is updated while contacted with the system and remains unchanged between contacts while the system evolves in time. After a prescribed number of such contacts, the position of the pointer is determined by means of a projective measurement. The outcome is specified in terms of a probability distribution function for unitary and Markovian dissipative dynamics and compared with the results of the same number of generalized Gaussian measurements of the considered observable. As a particular example, a qubit is considered with an observable contacting to the pointer that does not commute with the system Hamiltonian.

A method is proposed that allows one to infer the sum of the values of an observable taken during contacts with a pointer state. Hereby the state of the pointer is updated while contacted with the system and remains unchanged between contacts while the system evolves in time. After a prescribed number of such contacts the position of the pointer is determined by means of a projective measurement. The outcome is specified in terms of a probability distribution function for unitary and Markovian dissipative dynamics and compared with the results of the same number of generalized Gaussian measurements of the considered observable. As a particular example a qubit is considered with an observable contacting to the pointer that does not commute with the system Hamiltonian.

We study the quantum Brownian motion of a harmonic oscillator undergoing a sequence of generalized position measurements. Our exact analytical results capture the interplay of the measurement backaction and dissipation. Here we demonstrate that no freeze-in Zeno effect occurs upon increasing the monitoring frequency. A similar behavior is also found in the presence of generalized momentum measurements.