In this dissertation, a review of the concepts of quantum mechanics is presented, dealing with two-level systems (qubits) as part of a composite system, using the density matrix formalism. Using the method of Kraus operators, we study the evolution of systems subject to noise caused by the environment, such as in the case of the generalized amplitude damping channel. In order to be able to analyze the information obtained, a general review of Shannon and von Neumann entropies and their properties is made. A quantum view of thermodynamics is also presented, emphasizing the first and second laws of classical thermodynamics. The study focuses on studying the energetic processes that occur when a qubit is coupled to a thermal environment. The evolution of the composite system is described through a unitary transformation, and the thermodynamic properties of the qubit are analyzed through a more general definition of the first law of quantum thermodynamics, in which the role of quantum coherence is highlighted.
In this dissertation, a review of the concepts of quantum mechanics is presented, dealing with two-level systems (qubits) as part of a composite system, using the density matrix formalism. Using the method of Kraus operators, we study the evolution of systems subject to noise caused by the environment, such as in the case of the generalized amplitude damping channel. In order to be able to analyze the information obtained, a general review of Shannon and von Neumann entropies and their properties is made. A quantum view of thermodynamics is also presented, emphasizing the first and second laws of classical thermodynamics. The study focuses on studying the energetic processes that occur when a qubit is coupled to a thermal environment. The evolution of the composite system is described through a unitary transformation, and the thermodynamic properties of the qubit are analyzed through a more general definition of the first law of quantum thermodynamics, in which the role of quantum coherence is highlighted.
We study in this thesis composite quantum systems under the influence of external environments.In the first part of this work, we investigate a two qubit interacting system having one of them isolated and the other coupled to a thermal bath.We analyze the effect of the temperature of the bath on the dynamics of the two qubit system.In order to do that, we consider two different models of system-reservoir interaction: i) a "microscopic" model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a "phenomenological" approach, in which the master equation consists of a dissipative term added to the unitary evolution term.We show that in the strong coupling regime between the subsystems (qubits), the expected thermal equilibrium steady state for the two-qubit system naturally arises in the framework of the microscopic model, while in the phenomenological approach it is obtained a steady state density operator which is not correct.Furthermore, the differences are even more profound in the weak coupling regime, when the models give rise to opposite behaviors with regard to the linear entropy of qubit 1.At the context of quantum systems coupled to environments with few degrees of freedom, we solve analytically the matter-radiation interaction model known as two atom Tavis-Cummings Model.With the solutions at hand, achieved in general circumstances until the present not found in literature, in which the constituent atoms may be coupled with different strengths to the field and also have different frequency detunings, we study the effects that arise from the interaction of a small environment (atom in a statistical mixture state) with the other atom coupled to an oscillator (cavity mode).We show that nonclassical features associated to the main system may be significantly degraded by the action of the small environment, if atom 2 is resonantly coupled to the field.We also demonstrate that the nonclassical behaviour of the system may be restored if we detune the field from the transition frequency of atom 2, the environment.
Since the days of Boltzmann the foundation of thermodynamics has been subject to an ongoing discussion. Various problems like the precise definition of entropy, the origin of the second law, etc. have always been issues. For a long time the discussion has not been in the center of interest, for statistical physics work extremely well from a practical point of view. But now, as research deals with single small objects like molecules or atoms, the question arises whether or not thermodynamics are applicable to them, which leads back to the old question of the foundation of thermodynamics. We examine whether thermodynamics can be viewed as emerging from Schrödinger-type quantum dynamics. Therefore we partially transfer concepts of thermodynamical behavior in Gamma-space to the Hilbertspace of compound systems. Central roles play the local Von Neumann entropy of a system and the inevitability of entanglement with its environment, causing it to increase.
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.
The thermodynamics of quantum processes is a recent field of study and it has been growing in recent years. Previously thought of as an emergent phenomenon for macroscopic systems, thermodynamics started being applied to quantum systems considering quantities such as heat and work as stochastics. The peculiarity of these systems is that, in addition to studying energetic resources, we must also take into account quantum informational resources such as entanglement and coherence. In this scenario, entropy becomes an important quantity, because in addition to being related to the irreversibility of a process, it can also be used as a measure of the amount of information in the system to which we have access. Entropy, unlike energy, is not a conserved quantity; that is, in a closed system, there is not only an entropy flow between it\'s parts, but also, in general, entropy production. According to the principle of Landauer [IBM Journal of Research and Development, vol. 5, no. 3, pp. 183191 (1961)], it is the entropy produced that causes the loss of information. Studying, then, the production of entropy becomes important for areas such as quantum computing, where you want to have control over information gains and losses. In quantum processes, entropy is produced due both to changes in the energy of the system and to fluctuations in coherence [Phys. Rev. E 99, 042105 (2019); npj Quantum Information 5, 23 (2019)], a purely quantum resource. In this project, we propose to study the statistics of entropy production due to coherence. For this, we will investigate two different splittings of the entropy production: the one proposed in [Phys. Rev. E, vol. 99, 042105 (2019); npj Quantum Information 5, 23 (2019)] and a most recent one proposed in [Phys. Rev. Research 2, 023377 (2020); New Journal of Physics 23, 063027 (2021)]. For simplicity, we will analyse a unitary quantum process, using the two-point measurement (TPM) scheme [Phys. Rev. E 75, 050102 (2007)]. We will apply both formalisms for two specific quantum systems: a macrospin model and the Lipkin-Meshkov-Glick (LMG) model [Nuclear Physics, vol. 62, no. 2, pp. 188 224 (1965)]. We will analyse, in these cases, how the distribution of coherence depends on parameters such as system dimension, temperature, evolution in time, etc.
In conventional thermodynamics, a macroscopic process is characterized by changes in thermodynamic variables such as temperature, pressure, and entropy. In quantum thermodynamics, the state of a system is described by a density operator ρ, and the entropy of the system is given by the von Neumann entropy S = -k_B Tr(ρ ln ρ). Recent theoretical investigations have suggested that quantum coherence and phase correlations can also be thermodynamically relevant. This paper introduces the concept of Quantum Thermodynamic Phase Transfer (QTPT), a formalism that treats the quantum phase φ_T as a thermodynamic variable that can change during a process. We propose a set of postulates that extend the first and second laws of thermodynamics to include a term that accounts for the work associated with changes in φ_T. The framework is illustrated with a simple two–level system coupled to a thermal bath and driven by a time–dependent phase. We derive expressions for the generalized free energy and the entropy production that include phase contributions. The implications of QTPT for quantum heat engines, quantum refrigeration, and the fundamental limits of quantum thermodynamic cycles are discussed. The potential for a Nobel–level recognition of the unification of quantum coherence with classical thermodynamic principles is highlighted.
A área da termodinâmica quântica surgiu com o objetivo de identificar como conceitos e princípios da termodinâmica clássica, aplicada em sistemas macroscópicos, podem ser generalizados para aplicação em sistemas quânticos. Nessa perspectiva, é comum imaginar o sistema quântico aberto como uma máquina, cuja operação ocorre na presença de um ambiente que nem sempre encontra-se em um estado de equilíbrio térmico. Outro aspecto distinto da termodinâmica usual é o fato desse ambiente ter que ser tratado como um sistema quântico em diversas situações de interesse atual. Neste trabalho estudamos um universo quântico composto por um sistema de dois níveis (que faz a vez do sistema quântico aberto) interagindo com um pulso de fóton único (que desempenha o papel de ambiente do nosso sistema de interesse). Seguindo a prescrição adotada na literatura para interpretar as trocas energéticas nas formas de calor e trabalho, verificamos que a interação entre as partes do nosso universo quântico permite a observação dessas duas formas. Nessa dissertação, buscamos verificar como as condições impostas ao sistema interferem no trabalho, ou seja, como podemos alterar a quantidade e a taxa temporal com que o trabalho será executado. Essa verificação foi feita olhando para o comportamento da potência fixando o valor do trabalho e alterando o conjunto de parâmetros do sistema dos quais ela dependia. Dessa forma, conseguimos relacionar algumas mudanças no comportamento da potência devido a mudanças nos parâmetros do sistema.