Maximal work extraction from quantum systems

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 ...

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...

Ergotropy -- the maximal amount of unitarily extractable work -- measures the ``charge level'' of quantum batteries. We prove that in large many-body batteries ergotropy exhibits a concentration of measure phenomenon. Namely, the ergotropy of such systems is almost constant for almost all states sampled from the Hilbert--Schmidt measure. We establish this by first proving that ergotropy, as a function of the state, is Lipschitz-continuous with respect to the Bures distance, a...

We study the energy extraction from and charging to a finite-dimensional quantum system by general quantum operations. We prove that the changes in energy induced by unital quantum operations are limited by the ergotropy/charging bound for unitary quantum operations. This implies that, in order to break the ergotropy/charging bound for unitary quantum operations, one needs to perform a quantum operation with feedback control. We also show that the ergotropy/charging bound for...

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...

By computing the local energy expectation values with respect to some local measurement basis we show that for any quantum system there are two fundamentally different contributions: changes in energy that do not alter the local von Neumann entropy and changes that do. We identify the former as work and the latter as heat. Since our derivation makes no assumptions on the system Hamiltonian or its state, the result is valid even for states arbitrarily far from equilibrium. Exa...

Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely-positive and trace-preserving ma...

We investigate and ascertain the ideal inputs to any finite-time thermodynamic process. We demonstrate that the expectation values of entropy flow, heat, and work can all be determined via Hermitian observables of the initial state. These Hermitian operators encapsulate the breadth of behavior and the ideal inputs for common thermodynamic objectives. We show how to construct these Hermitian operators from measurements of thermodynamic output from a finite number of effectivel...

How much work can be extracted from a heat bath using a thermal machine? The study of this question has a very long tradition in statistical physics in the weak-coupling limit, applied to macroscopic systems. However, the assumption that thermal heat baths remain uncorrelated with physical systems at hand is less reasonable on the nano-scale and in the quantum setting. In this work, we establish a framework of work extraction in the presence of quantum correlations. We show i...