Dynamics of ergotropy and environment-induced work

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 optimise 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 concep...

We propose a new form of the Second Law inequality that defines a tight bound for extractable work from the non-equilibrium quantum state. In classical thermodynamics, the optimal work is given by the difference of free energy, what according to the result of Skrzypczyk \emph{et al.} can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and an ideal energy storage that is able to extract work from coherences. The n...

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...

Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum extractable work compatible with quantum mechanics (``ergotropy'') is derived and expressed in terms of the density matrix and the Hamiltonian. It is related to the property of majorization: more major states can provide more work. Scenarios of...

The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be extracted from a system by a unitary operation. In this analysis, we quantify how much ergotropy can be induced on a system as a result of system's interaction with a thermal bath, with a perspective of using it as a source of work performed by mi...

Here we study the impact of non-Markovian evolution on prominent characteristics of quantum thermodynamics, such as ergotropy and power. These are benchmarked by the behavior of the quantum speed limit time. We make use of both geometric-based, particularly quantum Fisher and Wigner-Yanase information metric, and physical properties based-measures, particularly relative purity measure and relative entropy of coherence measure, to compute the quantum speed limit time. A simple...

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of t...

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quant...

We put forth a notion of optimality for extracting ergotropic work, derived from an energy constraint governing the necessary dynamics for work extraction in a quantum system. Within the traditional ergotropy framework, which predicts an infinite set of equivalent pacifying unitaries, we demonstrate that the optimal choice lies in driving along the geodesic connecting a given state to its corresponding passive state. Moreover, in a practical scenario where unitaries are inevi...

Quantum open systems evolve according to completely positive, trace preserving maps acting on the density operator, which can equivalently be unraveled in term of so-called quantum trajectories. These stochastic sequences of pure states correspond to the actual dynamics of the quantum system during single realizations of an experiment in which the system's environment is monitored. In this chapter, we present an extension of stochastic thermodynamics to the case of open quant...