Maximal work extraction from quantum systems

The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix, subject to known constraints. In conjunction with the master equation for the density matrix, these two ingredients allow us to formulate the second law of thermodynamics in its widest possible setting. Thus problems arising in both quantu...

We study the maximal amount of energy that can be extracted from a finite quantum system by means of projective measurements. For this quantity we coin the expression "metrotropy" $\mathcal{M}$, in analogy with "ergotropy" $\mathcal{W}$, which is the maximal amount of energy that can be extracted by means of unitary operations. The study is restricted to the case when the system is initially in a stationary state, and therefore the ergotropy is achieved by means of a permutat...

We study the role of the initial quantum coherence in coherent processes generated by an external control of some parameters by looking on the thermodynamic work done. We start by taking in exam an active state and we isolate the contribution to the ergotropy coming from the quantum coherence among the energy eigenstates. It is shown to be related to the quantum relative entropy of coherence through an inequality which involves the completely passive state connected to the in...

Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic properties with those of the well - established approaches. Due to the non-negligible coupling to the heat reservoir, these systems are non-extensive by nature, and the former task may require the use of non-extensive parameter dependent inf...

We consider the amount of work which can be extracted from a heat bath using a bipartite state shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. For pure states the work deficit is exactly equal to the distillable entanglement of the state, and this is also achievable for maximally correlated ...

The concept of thermal machines has evolved from the canonical steam engine to the recently proposed nanoscopic quantum systems as working fluids. The latter obey quantum open system dynamics and frequently operate in non-equilibrium conditions. However, the role of this dynamics in the overall performance of quantum heat engines remains an open problem. Here, we analyse and optimize the efficiency and power output of two-stage quantum heat engines fuelled by non-equilibrium ...

Quantum thermodynamic process involves manipulating and controlling quantum states to extract energy or perform computational tasks with high efficiency. There is still no efficientgeneral method to theoretically quantify the effect of the quantumness of coherence and entanglement in work extraction. In this work, we propose a thermodynamics speed to quantify theextracting work. We show that the coherence of quantum systems can speed up work extractingwith respect to some cyc...

The interplay between quantum-mechanical properties, such as coherence, and classical notions, such as energy, is a subtle topic at the forefront of quantum thermodynamics. The traditional Carnot argument limits the conversion of heat to work; here we critically assess the problem of converting coherence to work. Through a careful account of all resources involved in the thermodynamic transformations within a fully quantum-mechanical treatment, we show that there exist therma...

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 $1/\sqrt{N}$. 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 $\mathcal{W}$ can be obtained almost d...

If the second law of thermodynamics forbids a transition from one state to another, then it is still possible to make the transition happen by using a sufficient amount of work. But if we do not have access to this amount of work, can the transition happen probabilistically? In the thermodynamic limit, this probability tends to zero, but here we find that for finite-sized systems, it can be finite. We compute the maximum probability of a transition or a thermodynamical fluctu...