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Relation Between Correlation and Energy in Quantum Thermodynamics

Bakhshinezhad, Faraj | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52586 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rezakhani, Ali; Huber, Marcus; Jafari, Akbar
  7. Abstract:
  8. Quantum thermodynamics is a new field of study in physics, which by considering the fundamentals of statistical mechanics, open quantum system, quantum information and mesoscopic system aims at the investigation of quantum systems from a thermodynamical point of view. To achieve these aims, a better understanding of the relations between quantum and thermodynamics fundamentals is essential. Energy and correlation are two key concepts in statistical mechanics and quantum thermodynamics (and information), respectively, that studying the relation between them will shed light on the fundamentals of quantum thermodynamics. As generating any correlation in quantum systems with initial heat state comes along with thermodynamic costs, in this dissertation we investigate the relation between energy and correlation in more details. Furthermore, by finding the upper bound for generating the correlation, we study the optimal unitary process when converting energy to correlation in bipartite and some multipartite systems. To do so, we put forward a framework for studying the process of optimally correlating identical (thermal) quantum systems. The framework is based on decompositions into subspaces that each support only states with diagonal (classical) marginals. Using methods from stochastic majorisation theory, we show that the creation of correlations at minimal energy cost is possible for all pairs of three- and four-dimensional quantum systems. For higher dimensions we provide sufficient conditions for the existence of such optimally correlating operations, which we conjecture to exist in all dimensions. As the next step, We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. we next discuss the emergence of the second law of thermodynamics under certain—but fairly general—conditions such as the Markovian assumption
  9. Keywords:
  10. Quantum Thermodynamics ; Energy ; Quantum Information Theory ; Second Law Thermodynamics Efficiency ; Binding Energy ; Classical and Quantum Correlation ; Passive State

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