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Investigation of Connection between Non-Markovianity of an Open Quantum System Evolution and its Thermodynamic Properties

Mohammadi, Amin | 2025

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 58424 (03)
  4. University: Sharif University of Technology
  5. Department: Chemistry
  6. Advisor(s): Shafiee, Afshin
  7. Abstract:
  8. In recent years, efforts to extend thermodynamic concepts to systems far smaller than the thermodynamic limit and to include quantum effects have led to the emergence of a new field known as quantum thermodynamics. Beyond its foundational importance in generalizing the laws of classical thermodynamics to the quantum regime, advances in experimental capabilities and the advent of nanoscale technologies have underscored the need for a deeper understanding of the thermodynamic behavior of small-scale systems. In parallel, growing evidence suggests that quantum effects play a significant role in various biological processes, further highlighting the relevance of quantum thermodynamics to such systems. One of the central notions in quantum thermodynamics is the concept of extractable work, which characterizes the maximum amount of work that can be drawn from a quantum system. In this thesis, using the definition based on the difference between non-equilibrium and equilibrium free energy, we investigate the time evolution of extractable work under a general quantum process represented by a completely positive and trace-preserving (CPTP) map. We derive a fundamental thermodynamic equation that expresses energy changes in a unified framework, incorporating heat, entropy, and extractable work, and thus integrates the first and second laws of thermodynamics. We then identify the reversible and irreversible components of this process and show how they correspond, respectively, to heat flow and changes in extractable work. Furthermore, by analyzing the relationship between quantum non-Markovianity and quantum coherence with extractable work dynamics, we identify these features as genuine quantum resources. The results are examined in the context of two practical examples involving two distinct models of quantum batteries. In the next step, we employ the resource-theoretic framework of thermodynamics to explore the role of quantum features in the process of ion transport across cell membranes. Within this framework, quantum properties are regarded as resources constrained by generalized thermodynamic laws in the quantum regime. Specifically, our findings show that non-Markovianity—manifesting as memory effects in ion transport dynamics—acts as a key quantum resource that enhances the yield and efficiency of the transport process. In contrast, quantum coherence—emerging as the superposition of energy states in ion-transport proteins—reduces these quantities, yet plays a critical role in distinguishing between ion channels and ion pumps, which represent two functionally distinct classes of ion-transport proteins in cell membranes. Finally, we demonstrate that introducing an additional coherent system enables the transformation of an ion pump into a channel via quantum coherence
  9. Keywords:
  10. Quantum Thermodynamics ; Quantum Coherence ; Thermodynamic Resource Theory ; Extractable Work ; Quantum Non-Markovianity ; Yield And Efficiency of Ion Transport Across Cell Membranes

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