The presence of correlations in the input state of a noninteracting many-body quantum system can lead to an increase in the amount of work we can extract from it under global unitary processes (ergotropy). The present work explores such effect on translationally invariant systems relying on the matrix product operator formalism to define a measure of how much they are correlated. We observe that in the thermodynamic limit of large number of sites, complete work extraction can be attained for relatively small correlation strength (a reduction of a 2 factor in dB units). Most importantly, such an effect appears to not be associated with the presence of quantum correlations (e.g., entanglement) in the input state (classical correlation suffices), and to be attainable by only using incoherent ergotropy. As a byproduct of our analysis, we also present a rigorous formulation of the heuristic typicality argument first formulated by Alicki and Fannes [R. Alicki and M. Fannes, Phys. Rev. E 87, 042123 (2013)], which gives the maximum work that is extractable for a set of many identical quantum systems in the asymptotic limit.
The presence of correlations in the input state of a noninteracting many-body quantum system can lead to an increase in the amount of work we can extract from it under global unitary processes (ergotropy). The present work explores such effect on translationally invariant systems relying on the matrix product operator formalism to define a measure of how much they are correlated. We observe that in the thermodynamic limit of large number of sites, complete work extraction can be attained for relatively small correlation strength (a reduction of a 2 factor in dB units). Most importantly, such an effect appears to not be associated with the presence of quantum correlations (e.g., entanglement) in the input state (classical correlation suffices), and to be attainable by only using incoherent ergotropy. As a byproduct of our analysis, we also present a rigorous formulation of the heuristic typicality argument first formulated by Alicki and Fannes [R. Alicki and M. Fannes, Phys. Rev. E 87, 042123 (2013)], which gives the maximum work that is extractable for a set of many identical quantum systems in the asymptotic limit.
Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the instantaneous energy eigenbasis of the dynamical system. Thermodynamic cycles can, in principle, be designed to extract work from this nonequilibrium resource. Here, we isolate and study the quantum coherent component to the work yield in such protocols. Specifically, we identify a coherent contribution to the ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters). We show this by dividing the optimal transformation into an incoherent operation and a coherence extraction cycle. We obtain bounds for both the coherent and incoherent parts of the extractable work and discuss their saturation in specific settings. Our results are illustrated with several examples, including finite-dimensional systems and bosonic Gaussian states that describe recent experiments on quantum heat engines with a quantized load.
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.
Abstract We investigate how the presence of quantum correlations can influence work extraction in closed quantum systems, establishing a new link between the field of quantum non-equilibrium thermodynamics and the one of quantum information theory. We consider a bipartite quantum system and we show that it is possible to optimize the process of work extraction, thanks to the correlations between the two parts of the system, by using an appropriate feedback protocol based on the concept of ergotropy. We prove that the maximum gain in the extracted work is related to the existence of quantum correlations between the two parts, quantified by either quantum discord or, for pure states, entanglement. We then illustrate our general findings on a simple physical situation consisting of a qubit system.
The paradigm of extracting work from an isolated quantum system through a cyclic Hamiltonian process is a topic of immense research interest. The optimal work extracted under such a process is termed ergotropy [Europhys. Lett. 67, 565 (2004)]. Here, in a multiparty scenario, we consider only a class of such cyclic processes that can be implemented locally, giving rise to the concept of local ergotropy. Eventually, the presence of quantum correlations results in a nonvanishing thermodynamic quantity called an ergotropic gap, measured by the difference between global and local ergotropy. However, the converse does not hold in general, i.e., its nonzero value does not necessarily imply the presence of quantum correlations. For arbitrary multiparty states, we quantify this gap. We also evaluate the difference between maximum global and local extractable work for arbitrary states when the system is no longer isolated but put in contact with a bath of the same local temperature.
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.
Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work extractable is equal to the ergotropy. Thus, we aim to identify and investigate the contributions to the ergotropy coming from different kinds of initial correlations (total, classical, discord, and entanglement correlations). By doing so, we have introduced and studied quantifiers of correlations which are based on ergotropy. In particular, our results suggest that only discord correlations always give a positive contribution to work extraction, whereas total, classical, and entanglement correlations can reduce the work extraction.