Abstract:
In this thesis, we explore the nonequilibrium thermodynamics of open quantum systems and its applications to quantum devices.
Many-body open quantum systems can host exotic phases of matter.
A particularly relevant example is the time-crystal phase, in which the time-translation symmetry of the dynamical generator is spontaneously broken.
This novel nonequilibrium phase manifests in persistent and stable oscillations of an order parameter of the system.
It has gathered significant interest and has shown promising potential applications, for instance in quantum engines and quantum metrology.
However, the thermodynamics of these time crystals remains largely unexplored, essentially due to their nonequilibrium nature.
This poses serious challenges in evaluating their potential in real-world applications.
In particular, systems exhibiting a time-crystal phase are typically described by phenomenological master equations, in which the coupling between the system and its surroundings is simplified by neglecting the influence of external energy sources and the internal interactions among particles within the many-body system.
However, it is known that these master equations can violate the laws of thermodynamics if the relevant thermodynamic quantities are not properly defined.
To address this open problem, in this thesis, we investigate the thermodynamics of time-crystal phases in our first and third publications.
In our first work, we propose a thermodynamic description for nonequilibrium open quantum systems described by phenomenological master equations.
Specifically, we consider that Hamiltonian contributions such as laser driving do not count as internal energy terms but rather they represent an input energy source, which allows us to formulate the first law in terms of an energy balance of the persistent nonequilibrium heat currents.
Using this idea, we propose a statement of the second law for systems described by phenomenological master equations.
We apply these results to an autonomous quantum engine driven by the time-crystal phase and demonstrate that its efficiency can be properly defined and is supported by a well-defined second law.
In our third publication, we analyze the thermodynamics of coupled systems, both of which can exhibit a time-crystal phase.
To characterize the thermodynamics of the coupled systems, we exploit a collision-model approach, which assumes a specific structure for the environment and the system-environment interaction that leads to phenomenological master equations.
Our findings also show that the time-crystal phase can be effectively used for energy storage applications.
In our second publication, we focus on open quantum systems undergoing an adiabatic evolution, where a parameter of the system is slowly varied.
This class of dynamics is relevant in many applications, including Carnot's engine cycles and dissipative quantum computation.
The interaction between the system and environment manifests as random jumps, such as photon emissions, which give rise to stochastic trajectories, each one related to a single experimental run.
In this regard, it is important to characterize not only the average values of observables related to these quantum jumps, but also their fluctuations.
In thermodynamic applications, an important observable is the stochastic heat, where a photon exchanged with the environment represents a discrete amount of heat dissipated or absorbed by the system.
The statistics of emissions-related observables can be described through the theory of large deviations, which provides tools to compute asymptotic probability distributions in the limit of long evolution times.
This theory captures the statistics of rare events, not explained by the central-limit theorem, and shows how to design systems where typical behavior mirrors the rare behavior of an original system.
In our second work, we rigorously derive, for the first time, the large-deviation behavior for quantum systems undergoing adiabatic dynamics.
Among our results, we show that the time evolution of stochastic observables follows a temporal additive principle, meaning that the total probability distribution is obtained by the composition of the instantaneous ones which all can be described by large deviation theory.
