Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown.Here we present a systematic study of these interplays in the case of driven Hubbard chains subject to a variety of interaction (from non-interacting to strongly correlated) and dynamical regimes (from sudden quench to quasi-adiabatic), and discuss which effects all these ingredients have on the work extraction and entropy production.As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting.We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy production, even when many-body correlations are significant.
Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown.Here we present a systematic study of these interplays in the case of driven Hubbard chains subject to a variety of interaction (from non-interacting to strongly correlated) and dynamical regimes (from sudden quench to quasi-adiabatic), and discuss which effects all these ingredients have on the work extraction and entropy production.As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting.We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy production, even when many-body correlations are significant.
Abstract Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many-body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown. Here we present a systematic study of these interplays in the case of driven Hubbard chains subject to a variety of interaction (from non-interacting to strongly correlated) and dynamical regimes (from sudden quench to quasi-adiabatic), and discuss which effects all these ingredients have on the work extraction and entropy production. As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting. We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy production, even when many-body correlations are significant.
Relatively small many-body quantum systems are often used as hardware for quantum devices. Most of these devices will operate below the thermal limit where thermodynamics must be treated differently to account for quantum behaviours. It is therefore imperative that the thermodynamic properties of these systems are well understood, especially as they can limit the technologies but also help the fabrication and running of efficient quantum devices. \n \nIn this thesis we study quantum work and entropy production in closed many-body quantum systems out-of-equilibrium. We find that, for the systems studied, the largest average quantum work can be extracted in adiabatic weakly correlated regimes. These regimes are also seen to minimise the entropy produced, making them efficient regimes in which to operate devices based on these systems. \n \nAdiabatic evolutions are important for many quantum devices, and so it is important that they can be accurately characterised. The validity of current methods has been questioned recently, so in this thesis we propose the use of metrics as a good quantitative measure to characterise adiabaticity. We found that the density distance (a more accessible quantity than the wavefunction and its distance measures) alone can determine adiabaticity in a range of quantum systems, even at finite temperature. \n \nHowever, when calculating properties of many-body systems, there are many challenges often resulting in the need to approximate. In this thesis we propose a new style of approximation for quantum thermodynamic properties, taking inspiration from density functional theory (DFT). This new style uses the exact initial state of the system but approximates the dynamics and is seen to be computationally cheap but largely accurate. We test this with non-interacting and DFT approximated dynamics, finding that, surprisingly, the non-interacting dynamics give the most accurate results in most regimes, with the cheapest cost.
The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of the system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a nonequilibrium dynamics. By driving transient currents to oppose the precursor to the metal-Mott-insulator transition in a diversity of dynamical regimes, we show how increasing many-body interactions dramatically affect the statistics of energy fluctuations and, consequently, the extractable work distribution of finite Hubbard chains. Statistical properties of such distributions as its skewness with its impressive change across the transition can be related to irreversibility and entropy production. Even for slow driving rates, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong features in the work distribution. In the Mott-insulating phase, the work fluctuation-dissipation balance gets modified with the irreversible entropy production dominating over work fluctuations. Because of this, effects of an interaction-driven quantum phase transition on thermodynamic quantities and irreversibility must be considered in the design of protocols in small-scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols on a quantum scale.
Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble, reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.
The fabrication, utilisation, and efficiency of quantum technology devices rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between particles make the complexity of related calculations grow exponentially with the system size. Here we explore and systematically compare 'simple' and 'hybrid' approximations to the average work and entropy variation built on static density functional theory concepts. These approximations are computationally cheap and could be applied to large systems. We exemplify them considering driven one-dimensional Hubbard chains and show that, for 'simple' approximations and low to medium temperatures, it pays to consider a good estimate of the Kohn-Sham Hamiltonian to approximate the driving Hamiltonian. Our results confirm that a 'hybrid' approach, requiring a very good approximation of the initial and, for the entropy, final states of the system, provides great improvements. This approach should be particularly efficient when many-body effects are not increased by the driving Hamiltonian.
In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems. The method is articulated in various approximation protocols which allow to achieve increasing levels of accuracy, it is relatively simple to implement even for medium and large number of interactive particles, and uses tools and concepts from density functional theory. We test the method on the driven Hubbard dimer at half filling, and compare exact and approximate results. We show that the proposed method reproduces the average quantum work to high accuracy: for a very large region of parameter space (which cuts across all dynamical regimes) estimates are within 10% of the exact results.