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Quantum operator entropies under unitary evolution.

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  • 1Department of Physics and Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA.

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PubMed
Summary
This summary is machine-generated.

Quantum operator entropy explains how entropy increases during reversible evolution, aligning with thermodynamics. This quantum information measure resolves the paradox of constant von Neumann entropy in unitary time evolution.

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Thermodynamics

Background:

  • The von Neumann entropy remains constant during unitary Schrödinger time evolution, seemingly contradicting the second law of thermodynamics.
  • Quantum operator entropy, introduced by Ingarden, measures missing information about an observable within a quantum state.

Purpose of the Study:

  • To investigate the apparent conflict between constant von Neumann entropy and the increasing entropy observed in thermodynamics.
  • To analyze the behavior of quantum operator entropy in a model system undergoing reversible unitary evolution.

Main Methods:

  • Examined pure state unitary evolution in a model system with interconnected, topologically disordered states and a time-independent Hamiltonian.
  • Simulated the free expansion of an initially confined quantum state into available states.
  • Applied no coarse-graining, ensuring the reversibility of time development and preservation of quantum information.

Main Results:

  • The positional entropy was observed to increase over time during the free expansion.
  • This increase in positional entropy is consistent with classical statistical mechanics and the second law of thermodynamics.
  • The system demonstrated completely reversible time development without any loss of quantum information.

Conclusions:

  • Quantum operator entropy provides a framework to understand entropy increase in quantum systems even under reversible unitary evolution.
  • The study reconciles the constancy of von Neumann entropy with the macroscopic observation of increasing entropy.
  • The findings support the applicability of thermodynamic principles to quantum information dynamics.