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Modeling mechanical equilibration processes of closed quantum systems: A case study.

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This study models a quantum particle in a box undergoing spontaneous thermodynamic changes. It captures the interplay between quantum system dynamics and classical wall motion during compression and expansion.

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Area of Science:

  • Quantum thermodynamics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Understanding thermodynamic transformations in quantum systems is crucial.
  • Modeling spontaneous processes requires considering system-environment interactions.
  • Classical approximations for macroscopic parameters can simplify complex quantum dynamics.

Purpose of the Study:

  • To model the dynamics of a closed quantum system undergoing spontaneous thermodynamic transformations.
  • To investigate the thermodynamics of quantum systems with moving boundaries.
  • To develop a model that captures the mutual interactions between quantum dynamics and macroscopic parameters.

Main Methods:

  • Modeling a quantum particle in a box with a moving, insulating wall.
  • Assuming classical dynamics for the wall's motion.
  • Deriving a system of differential equations for coupled quantum and classical evolution.
  • Analyzing the thermodynamics of compression and expansion processes.

Main Results:

  • A model describing the coupled dynamics of a quantum system and its classical boundary.
  • The ability to capture key properties of thermodynamic transformations.
  • Demonstration of how quantum system evolution influences wall motion and vice versa.
  • Insights into non-equilibrium quantum thermodynamics.

Conclusions:

  • The developed model provides a more comprehensive description than ad hoc time-dependent Hamiltonians.
  • It highlights the importance of mutual interactions in quantum thermodynamic processes.
  • The approach is applicable to studying spontaneous, non-driven transformations in quantum mechanics.