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