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arXiv:1806.11384 · Physical review. E

Simple scheme for extracting work with a single bath

Nicolò Piccione, Benedetto Militello, Anna Napoli, Bruno Bellomo

Published Sep 27, 2019• 8 citations
arXivHTMLPDF

Abstract

We propose a simple protocol exploiting the thermalization of a storage bipartite system S to extract work from a resource system R. The protocol is based on a recent work definition involving only a single bath. A general description of the protocol is provided without specifying the characteristics of S. We quantify both the extracted work and the ideal efficiency of the process, also giving maximum bounds for them. Then, we apply the protocol to two cases: two interacting qubits and the Rabi model. In both cases, for very strong couplings, an extraction of work comparable with the bare energies of the subsystems of S is obtained and its peak is reached for finite values of the bath temperature, T. We finally show, in the Rabi model at T=0, how to transfer the work stored in S to an external device, permitting thus a cyclic implementation of the whole work-extraction protocol. Our proposal makes use of simple operations not needing fine control.

DOI
10.1103/physreve.100.032143

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We propose a simple protocol exploiting the thermalization of a storage bipartite system S to extract work from a resource system R. The protocol is based on a recent work definition involving only a single bath. A general description of the protocol is provided without specifying the characteristics of S. We quantify both the extracted work and the ideal efficiency of the process, also giving maximum bounds for them. Then, we apply the protocol to two cases: two interacting qubits and the Rabi model. In both cases, for very strong couplings, an extraction of work comparable with the bare energies of the subsystems of S is obtained and its peak is reached for finite values of the bath temperature, T. We finally show, in the Rabi model at T=0, how to transfer the work stored in S to an external device, permitting thus a cyclic implementation of the whole work-extraction protocol. Our proposal makes use of simple operations not needing fine control.
We propose a protocol which exploits the collective thermalisation of a bipartite system to extract work from another system. The protocol is based on a recently proposed work definition not requiring measurements and involving the presence of a single bath. A general description of the protocol is provided without specifying the characteristics of the bipartite system. We quantify both the extracted work and the ideal efficiency of the process also giving a maximum bound to the extracted work. Then, we apply the protocol to the case when the bipartite system is governed by the Rabi Hamiltonian while using a zero temperature bath. For very strong couplings, an extraction of work comparable with the typical energies of the subsystems and an efficiency greater than one half can be obtained.
This extended abstract contains an outline of the work reported at the conference IQIS2018. We show that it is possible to exploit a thermalization process to extract work from a resource system R to a bipartite system S. To do this, we propose a simple protocol in a general setting in the presence of a single bath at temperature T and then examine it when S is described by the quantum Rabi model at T = 0 . We find the theoretical bounds of the protocol in the general case and we show that when applied to the Rabi model it gives rise to a satisfactory extraction of work and efficiency.
We show that work can be extracted from a two-level system (spin) coupled to a bosonic thermal bath. This is possible due to different initial temperatures of the spin and the bath, both positive (no spin population inversion), and is realized by means of a suitable sequence of sharp pulses applied to the spin. The extracted work can be of the order of the response energy of the bath, therefore much larger than the energy of the spin. Moreover, the efficiency of extraction can be very close to its maximum, given by the Carnot bound, at the same time the overall amount of the extracted work is maximal. Therefore, we get a finite power at efficiency close to the Carnot bound. The effect comes from the back-reaction of the spin on the bath, and it survives for a strongly disordered (inhomogeneously broadened) ensemble of spins. It is connected with generation of coherences during the work-extraction process, and we deduced it in an exactly solvable model. All the necessary general thermodynamical relations are deduced from the first principles of quantum mechanics and connections are made with processes of lasing without inversion and with quantum heat engines.
Abstract We revisit the problem of work extraction from a system in contact with a heat bath to a work storage system, and the reverse problem of state formation from a thermal system state in single-shot quantum thermodynamics. A physically intuitive and mathematically simple approach using only elementary majorization theory and matrix analysis is developed, and a graphical interpretation of the maximum extractable work, minimum work cost of formation, and corresponding single-shot free energies is presented. This approach provides a bridge between two previous methods based respectively on the concept of thermomajorization and a comparison of subspace dimensions. In addition, a conceptual inconsistency with regard to general work extraction involving transitions between multiple energy levels of the work storage system is clarified and resolved. It is shown that an additional contribution to the maximum extractable work in those general cases should be interpreted not as work extracted from the system, but as heat transferred from the heat bath. Indeed, the additional contribution is an artifact of a work storage system (essentially a suspended ‘weight’ that can be raised or lowered) that does not truly distinguish work from heat. The result calls into question the common concept that a work storage system in quantum thermodynamics is simply the quantum version of a suspended weight in classical thermodynamics.
We address the problem of extracting work from a quantum system assisted by a quantum non-demolition (QND) energy measurement. When a perfect QND measurement can be performed and an auxiliary zero-temperature bath is available, the full energy of the quantum state can in principle be extracted even without any prior information on the input state. Owing to the presence of a zero-temperature bath, this is achieved at no energetic cost for the measurement process itself. On the contrary, here we consider what happens when the same protocol is implemented in non-ideal scenarios, specifically when the auxiliary bath has a finite temperature. In this case, not only is it impossible to extract the entire energy from the system, but the measurement strategy also acquires a non-zero energetic cost, accounting for both the interaction between system and measurement apparatus, and the corresponding Landauer erasure cost. We quantitatively assess the performance of these work-extraction protocols, both in absolute terms and through the so-called daemonic net gain, which explicitly includes the energetic cost of the measurement. We rigorously prove that, when access to a thermal bath is allowed in the extraction protocol, the daemonic net gain is always non-positive for any temperature of the auxiliary bath. Conversely, when only unitary operations are considered, the daemonic net gain can attain positive values. We further discuss these different figures of merit by analyzing a paradigmatic example for a single qubit system.
We consider locally thermal states (for two qubits) with certain amount of quantum entanglement present between them. Unlike previous protocols we show how work can be extracted by performing local unitary operations on this state by allowing those two qubits to interact with thermal baths of different temperatures, thereby gradually removing the entanglement between them till they reach a direct product state. Also we demonstrate that, further work can be extracted from this direct product state by performing global unitary operation, thereby establishing that work can be extracted from a system composed of locally thermal subsystems even after removing quantum correlations between them if the subsystems are thermalized at different temperatures. Also we show that even if we consider a initial state where there is no entanglement between the two qubits, we can also extract work locally using our method.