Abstract We consider work extraction from N copies of a quantum system. When the same work-extraction process is implemented on each copy, the relative size of fluctuations is expected to decay as <?CDATA $1/\sqrt{N}$?> 1 / N . Here, we consider protocols where the copies can be processed collectively, and show that in this case work fluctuations can disappear exponentially fast in N . As a consequence, a considerable proportion of the average extractable work <?CDATA ${ \mathcal W }$?> can be obtained almost deterministically by globally processing a few copies of the state. This is derived in the two canonical scenarios for work extraction: (i) in thermally isolated systems, where <?CDATA ${ \mathcal W }$?> corresponds to the energy difference between initial and passive states, known as the ergotropy, and (ii) in the presence of a thermal bath, where <?CDATA ${ \mathcal W }$?> is given by the free energy difference between initial and thermal states.
Abstract We consider work extraction from N copies of a quantum system. When the same work-extraction process is implemented on each copy, the relative size of fluctuations is expected to decay as <?CDATA $1/\sqrt{N}$?> 1 / N . Here, we consider protocols where the copies can be processed collectively, and show that in this case work fluctuations can disappear exponentially fast in N . As a consequence, a considerable proportion of the average extractable work <?CDATA ${ \mathcal W }$?> can be obtained almost deterministically by globally processing a few copies of the state. This is derived in the two canonical scenarios for work extraction: (i) in thermally isolated systems, where <?CDATA ${ \mathcal W }$?> corresponds to the energy difference between initial and passive states, known as the ergotropy, and (ii) in the presence of a thermal bath, where <?CDATA ${ \mathcal W }$?> is given by the free energy difference between initial and thermal states.
Abstract We consider work extraction from N copies of a quantum system. When the same work-extraction process is implemented on each copy, the relative size of fluctuations is expected to decay as 1 / N . Here, we consider protocols where the copies can be processed collectively, and show that in this case work fluctuations can disappear exponentially fast in N. As a consequence, a considerable proportion of the average extractable work can be obtained almost deterministically by globally processing a few copies of the state. This is derived in the two canonical scenarios for work extraction: (i) in thermally isolated systems, where corresponds to the energy difference between initial and passive states, known as the ergotropy, and (ii) in the presence of a thermal bath, where is given by the free energy difference between initial and thermal states.
We consider the task of extracting work from quantum systems in the resource theory perspective of thermodynamics, where free states are arbitrary thermal states, and allowed operations are energy conserving unitary transformations. Taking as our work storage system a 'weight' we prove the second law and then present simple protocols which extract average work equal to the free energy change of the system - the same amount as in classical thermodynamics. Crucially, for systems in 'classical' states (mixtures of energy eigenstates) our protocol works on a single copy of the system. This is in sharp contrast to previous results, which showed that in case of almost-deterministic work extraction, collective actions on multiple copies are necessary to extract the free energy. This establishes the fact that free energy is a meaningful notion even for individual systems in classical states. However, for non-classical states, where coherences between energy levels exist, we prove that collective actions are necessary, so long as no external sources of coherence are used.
We consider a quasi-probability distribution of work for an isolated quantum system coupled to the energy-storage device given by the ideal weight. Specifically, we analyze a trade-off between changes in average energy and changes in weight's variance, where work is extracted from the coherent and incoherent ergotropy of the system. Primarily, we reveal that the extraction of positive coherent ergotropy can be accompanied by the reduction of work fluctuations (quantified by a variance loss) by utilizing the non-classical states of a work reservoir. On the other hand, we derive a fluctuation-decoherence relation for a quantum weight, defining a lower bound of its energy dispersion via a dumping function of the coherent contribution to the system's ergotropy. Specifically, it reveals that unlocking ergotropy from coherences results in high fluctuations, which diverge when the total coherent energy is unlocked. The proposed autonomous protocol of work extraction shows a significant difference between extracting coherent and incoherent ergotropy: The former can decrease the variance, but its absolute value diverges if more and more energy is extracted, whereas for the latter, the gain is always non-negative, but a total (incoherent) ergotropy can be extracted with finite work fluctuations. Furthermore, we present the framework in terms of the introduced quasi-probability distribution, which has a physical interpretation of its cumulants, is free from the invasive nature of measurements, and reduces to the two-point measurement scheme (TPM) for incoherent states. Finally, we analytically solve the work-variance trade-off for a qubit, explicitly revealing all the above quantum and classical regimes.
There has been an increasing interest in the quantification of nearly deterministic work extraction from a finite number of copies of microscopic particles in finite time. This paradigm, the so-called single-shot $\ensuremath{\epsilon}$-deterministic work extraction, considers processes with small failure probabilities. However, the resulting fluctuations in the extracted work entailed by this failure probability have yet to be studied. In the standard thermodynamics, paradigm fluctuation theorems are powerful tools to study fluctuating quantities. Given that standard fluctuation theorems are inadequate for a single-shot scenario, here we formulate and prove a fluctuation relation specific to the single-shot $\ensuremath{\epsilon}$-deterministic work extraction to bridge this gap. Our results are general in the sense that we allow the system to be in contact with the heat bath at all times. As a corollary of our theorem, we derive the known bounds on the $\ensuremath{\epsilon}$-deterministic work.
We investigate the dynamics of quantum ergotropy in a multipartite system of two-level atoms interacting with a quantized field. The role of multipartite quantum mutual information and quantum relative entropy is analyzed to understand how correlations and the distinguishability between the passive state and the product of local states affect the extractable work. Numerical results for systems containing two to five atoms show that the maximum ergotropy does not increase linearly with the system size, while the intervals of zero ergotropy are gradually modified and suppressed for larger systems. We also study the effect of the average thermal photon number and different initial atomic states. Increasing the thermal photon number mainly reduces the relative-entropy contribution, whereas the initial state strongly influences both the magnitude and persistence of ergotropy. Among the considered states, the partially entangled state provides the largest and more persistent extractable work, while the mixed GHZ state gives the smallest ergotropy. These results highlight the importance of multipartite correlations, thermal effects, and state preparation in controlling quantum work extraction and may be useful for future studies of quantum batteries and quantum power.
The amount of extractable work from a physical system is fundamentally connected to the information available about its state, as illustrated by Maxwell's demon and the Gibbs paradox. In standard thermodynamic protocols involving system--bath interactions, the maximum work is given by the free-energy difference between the initial state and the corresponding Gibbs state at the bath temperature. This motivates a natural question: does information also limit work extraction in closed quantum systems that do not involve a heat bath and where work is obtained through unitary operations generated by a time-dependent Hamiltonian? While ergotropy quantifies the maximum work extractable via unitary operations, it assumes complete knowledge of the quantum state, typically requiring full state tomography. In realistic scenarios, however, only partial information is accessible. In this case, the relevant figure of merit is observational ergotropy, which depends explicitly on the measurement used to probe the system. We show that observational ergotropy decreases under classical post-processing of measurement outcomes, implying that fine-grained measurements allow greater work extraction than coarse-grained ones. Moreover, maximizing observational ergotropy over all possible measurements recovers standard ergotropy, which decomposes into incoherent (classical) and coherent (quantum) contributions. Our results demonstrate that coherence in the measurement projectors constitutes the key resource, enabling work extraction beyond the incoherent limit and establishing coherence as the origin of quantum advantage in observational ergotropy extraction.