Work fluctuations in slow processes: quantum signatures and optimal control

The study of thermodynamic fluctuations allows one to relate the free energy difference between two equilibrium states with the work done on a system through processes far from equilibrium. This finding plays a crucial role in the quantum regime, where the definition of work becomes non-trivial. Based on these relations, here we develop a simple interferometric method allowing a direct estimation of the work distribution and the average dissipative work during a driven thermo...

We propose a definition of externally measurable quantum work in driven systems. Work is given as a quantum observable on a control device which is forcing the system and can be determined without knowledge of the system Hamiltonian $H_\mathcal{S}$. We argue that quantum work fluctuation theorems which rely on the knowledge of $H_\mathcal{S}$ are of little practical relevance, contrary to their classical counterparts. Using our framework, we derive a fluctuation theorem which...

In this thesis, I investigate various aspects of one of the most fundamental questions in thermodynamics: what state transformations can quantum systems undergo while interacting with a thermal bath under specific constraints? These constraints may involve total energy conservation, memory effects, or finite-size considerations. Addressing this question leads to (i) a characterisation of the structure of the thermodynamic arrow of time, (ii) a framework bridging the gap betwe...

In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian open quantum systems. We first consider three instructive examples and then systematically minimize the product of uncertainty and entropy production for small open quantum systems. As our main result, we find that the thermodynamic cost of re...

Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, a regime in which coherences and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we report an experimental measurement of the genuine quantum correction to the classical work fl...

The task of finding optimal protocols that minimize the energetic cost of thermodynamic processes of long yet finite duration $\tau$ is a pressing one. We approach this problem here in a rigorous and systematic fashion by means of the adiabatic perturbation theory of closed Hamiltonian quantum systems. Our main finding is a $1/\tau^2$ scaling of the excess work for large $\tau$ in gapped systems. This result is at odds with the $1/\tau$ prediction of the geometric approach to...

We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, non-Markovian effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by non-Ma...

In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous...

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can b...

Cooling of a quantum system is limited by the size of the control forces that are available (the "speed" of control). We consider the most general cooling process, albeit restricted to the regime in which the thermodynamics of the system is preserved (weak coupling). Within this regime, we further focus on the most useful control regime, in which a large cooling factor, and good ground-state cooling can be achieved. We present a control protocol for cooling, and give clear st...