Owen Maroney

Information and Entropy in Quantum Theory

Contents

  1. Introduction
  2. Information and Measurement
    1. Shannon Information
      1. Communication
      2. Measurements
    2. Quantum Information
      1. Quantum Communication Capacity
      2. Information Gain
      3. Quantum Information Quantities
      4. Measurement
    3. Quantum Measurement
    4. Summary
  3. Active Information and Interference
    1. The Quantum Potential as an Information Potential
      1. Non-locality
      2. Form dependance
      3. Active, Passive and Inactive Information 
    2. Information and Interference
      1. The basic interferometer
      2. Which way information
      3. Welcher-weg devices
      4. Surrealistic trajectories
      5. Conclusion
    3. Information and which path measurements
      1. Which path information
      2. Welcher weg information
      3. Locality and teleportation
      4. Conclusion
    4. Conclusion
  4. Entropy and Szilard's Engine
    1. Statistical Entropy
    2. Maxwell's Demon
      1. Information Acquisition
      2. Information Erasure
      3. "Demonless" Szilard Engine
    3. Conclusion
  5. The Quantum Mechanics of Szilard's Engine
    1. Particle in a box
    2. Box with Central Barrier
      1. Asymptotic solutions for HBA, V>>E
    3. Moveable Partition
      1. Free Piston
      2. Piston and Gas on one side
      3. Piston with Gas on both sides
    4. Lifting a weight against gravity
    5. Resetting the Engine
      1. Inserting Shelves
      2. Removing the Piston
      3. Resetting the Piston
    6. Conclusions
      1. Raising Cycle
      2. Lowering Cycle
      3. Summary
  6. The Statistical Mechanics of Szilard's Engine
    1. Statistical Mechanics
    2. Thermal state of gas
      1. No partition
      2. Partition raised
      3. Confined gas
      4. Moving partition
    3. Thermal state of weights
      1. Raising and Lowering Weight
      2. Inserting shelf
      3. Mean energy of projected weights
    4. Gearing ratio of piston to pulley
      1. Location of unraised weight
    5. The raising cycle
    6. The lowering cycle
    7. Energy flow in the Popper-Szilard Engine
    8. Conclusion
  7. The Thermodynamics of Szilard's Engine
    1. Free Energy and Entropy
      1. One Atom Gas
      2. Weight above height h
      3. Correlations and mixing
    2. Raising Cycle
    3. Lowering Cycle
    4. Conclusion
  8. Resolution of the Szilard Paradox
    1. The Role of the Demon
      1. The Role of the Piston
      2. Maxwell's Demons
      3. The Significance of Mixing
      4. Generalised Demon
      5. Conclusion
    2. Restoring the Auxiliary
      1. Fluctuation Probability Relationship
      2. Imperfect Resetting
      3. The Carnot Cycle and the Entropy Engine
      4. Conclusion
    3. Alternative Resolutions
      1. Information Acquisition
      2. Information Erasure
      3. "Free Will" and Computation
      4. Quantum Superposition
    4. Comments and Conclusions
      1. Criticisms of the Resolution
      2. Summary
  9. Information and Computation
    1. Reversible and tidy computation
      1. Landauer erasure
      2. Tidy classical computation
      3. Tidy quantum computation
      4. Conclusion
    2. Thermodynamic and logical reversibility
      1. Thermodynamically irreversible computation
      2. Logically irreversible operations
    3. Conclusion
  10. Active Information and Entropy
    1. The Statistical Ensemble
    2. The density matrix
      1. Szilard Box
      2. Correlations and Measurement
    3. Active Information
      1. The Algebraic Approach
      2. Correlations and Measurement
    4. Conclusion

Appendices