Intro; Supervisors' Foreword; Abstract; Acknowledgements; Contents; Acronyms; Part I Introduction to Open Quantum Systems and Quantum Thermodynamics; 1 Basic Concepts; 1.1 Quantum Mechanics; 1.1.1 The Density Operator; 1.1.2 Liouville-von Neumann Equation; 1.1.3 Heisenberg and Interaction Pictures; 1.1.4 The Microreversibility Principle; 1.1.5 Composite Quantum Systems; 1.1.6 Quantum Entropies; 1.1.7 Distance Measures; 1.2 Prototypical Systems; 1.2.1 The Qubit System; 1.2.2 Manipulation of Qubits by Classical Fields; 1.2.3 The Harmonic Oscillator; 1.2.4 Coherent States; 1.2.5 Squeezed States

1.3 Quantum Measurement1.3.1 Ideal Measurements; 1.3.2 Generalized Measurements; 1.3.3 Classes of Measurements; 1.4 Classical and Quantum Correlations; 1.4.1 Entanglement; 1.4.2 Mutual Information; 1.4.3 Quantum Discord; References; 2 Open Quantum Systems Dynamics; 2.1 Quantum Maps and Operations; 2.1.1 Properties of CPTP Maps; 2.1.2 Kraus Operator-Sum Representation; 2.1.3 Environmental Models; 2.1.4 Some Examples of CPTP Maps; 2.2 Markovian Master Equations; 2.2.1 The Lindblad Form; 2.2.2 The Born-Markov Master Equation; 2.3 Dissipative Qubits and Harmonic Oscillators

2.3.1 Qubit Relaxation in a Bosonic Environment2.3.2 Bosonic Collisional Model; 2.3.3 Quantum Brownian Motion; 2.4 Open Many-Body Systems; 2.4.1 Common Versus Independent Environmental Action; 2.4.2 Coupled Dissipative Harmonic Oscillators; 2.5 Quantum Trajectories; 2.5.1 Continuous Measurements and Quantum Jumps; 2.5.2 Stochastic Schrödinger Equation; 2.5.3 Master Equation Unraveling; References; 3 Quantum Thermodynamics; 3.1 Principles of Thermodynamics; 3.1.1 The First Law of Thermodynamics; 3.1.2 The Second Law of Thermodynamics; 3.1.3 Statistical Mechanics and Entropy

3.1.4 Helmholtz and Nonequilibrium Free Energy3.1.5 The Third Law of Thermodynamics; 3.1.6 Thermodynamics and Information; 3.2 Fluctuation Theorems; 3.2.1 Stochastic Thermodynamics; 3.2.2 Classical Fluctuation Theorems; 3.2.3 Quantum Fluctuation Theorems; 3.3 Quantum Thermal Machines; 3.3.1 Quantum Otto Cycle; 3.3.2 Autonomous Thermal Machines; 3.3.3 Quantum Effects in Thermal Machines; 3.4 Other Topics in Quantum Thermodynamics; 3.4.1 Equilibration and Thermalization; 3.4.2 Resource Theories in Quantum Thermodynamics; References

Part II Quantum Synchronization Induced by Dissipation in Many-Body Systems4 Transient Synchronization and Quantum Correlations; 4.1 Synchronization Phenomena and Previous Works; 4.2 Two Dissipative Harmonic Oscillators; 4.3 Synchronization; 4.4 Quantum Correlations; 4.5 Dependence on Initial Conditions; 4.6 Conclusions; References; 5 Noiseless Subsystems and Synchronization; 5.1 Prevention of Decoherence and Dissipation; 5.2 Three Oscillators in a Common Environment; 5.3 Noiseless Subsystems and Asymptotic Properties; 5.3.1 Asymptotic Entanglement; 5.3.2 Quantum Synchronization