Foundational Theoretical Issues of Quantum Heat Engines and Hot Entanglement

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We study open quantum systems in the contexts of quantum heat engines, refrigerators and quantum entanglement in systems in contact with high temperature reservoirs. Emphasizing the underlying theoretical foundations rather than practical aspects such as enhancement in efficiency of engines and refrigerators or in entanglement measures for a particular set of system and bath parameters, this work focuses on some important aspects of open quantum systems and quantum thermodynamics and provide in-depth analysis of them using relatively simple yet robust models in non- equilibrium statistical mechanics. These examples include a refrigerator for quantum many-body systems in the Markovian regime, a single harmonic oscillator quantum Otto cycle with its generalization to squeezed thermal baths and the entanglement dynamics of two coupled harmonic oscillators each having its own separate thermal baths in the non-Markovian regime. The investigation of these setups in a unified context in this dissertation also brings up the discussion on the validity of Markovian approximation for open quantum systems and the qualitative differences in Markovian versus non-Markovian open system dynamics, which is addressed on multiple occasions throughout the cases we study. Our analysis of quantum Otto cycle with squeezed thermal reservoirs show that the efficiency of the cycle does not change due to the squeezing in the bath in contrast to previous works studying the same cycle restricted by Markovian assumptions. In our investigation of the effects of time-dependent coupling in a system of two harmonic oscillators with two separate baths in both Markovian and non-Markovian regimes, we find that the driving-induced instability of the solutions of the Langevin equations of the oscillator system is necessary to sustain entanglement at late times with hot reservoirs which mayrender hot entanglement untenable. The effects of Markovianity/non-Markovianity, non-thermal reservoirs, contact with multiple reservoirs and time-dependent system Hamiltonians in quantum thermodynamics are addressed in this thesis.