Physicists have long known that it is possible to extract work from some quantum states but not others. These others are known as passive states. So the quantity physicists are interested in is the difference between the energy of the quantum system and its passive states. All that energy is potentially extractable to do work elsewhere.
Alicki and Fannes show that the extractable work is generally less than the thermodynamic limit. In other words, they show that this kind of system isn’t perfect. However, the twist is that Alicki and Fannes say things change if you have several identical quantum batteries that are entangled. Entanglement is a strange quantum link that occurs when separate particles have the same wavefunction. In essence, these particles share the same existence.
Alicki and Fannes show that when quantum batteries are entangled they become much better. That’s essentially because all the energy from all the batteries can be extracted at once. “Using entanglement one can in general extract more work per battery,” they say.
In fact, as the number of entangled batteries increases, the performance becomes arbitrarily close to the thermodynamic limit. In other words, a battery consisting of large numbers of entangled quantum batteries could be almost perfect.
That’s a fascinating result. Quantum batteries in the form of atoms or molecules may be ubiquitous in nature, in processes such as photosynthesis. Biologists know for example that during photosynthesis, energy is transferred with 100 per cent efficiency from one molecular machine to another.
Motivated by the recent interest in thermodynamics of micro- and mesoscopic quantum systems we study the maximal amount of work that can be reversibly extracted from a quantum system used to store temporarily energy. Guided by the notion of passivity of a quantum state we show that entangling unitary controls extract in general more work than independent ones. In the limit of large number of copies one can reach the thermodynamical bound given by the variational principle for free energy.
The notion of maximal reversibly extractable work for a quantum battery motivated by the concept of passivity is presented. It is applicable to full quantum models of micro- or mesoscopic machines where work is supplied or extracted by a quantum system (‘quantum battery’, ‘work reservoir’) instead of a time-dependent perturbation of the Hamiltonian. A proper deﬁnition of work is important to develop a consistent thermodynamics of small quantum systems which is relevant in nanotechnology and biophysics. Generally, the extractable work is smaller than the thermodynamical bound computed using variational principle for a free energy. Using entanglement one can in general extract more work per battery from several independent copies of a battery and asymptotically reach the thermodynamical bound. However, the optimal procedures of work extraction are generally diﬃcult to implement by realistic control Hamiltonians. An interesting problem for future investigation is to ﬁnd eﬃciency bounds when practical restrictions are imposed on the available control mechanisms.
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