The Physics of Information

1. The Physics of Information 2 2. Thermodynamics 4 2.1. The laws 5 2.2. Free energy 8 3. Statistical mechanics 9 3.1. Definitions and postulates 10 3.2. Counting microstates for a system of magnetic spins 11 3.3. The Maxwell-Boltzmann-Gibbs distribution 12 3.4. Free energy revisited 13 3.5. Gibbs entropy 13 4. Nonlinear dynamics 15 4.1. The ergodic hypothesis 16 4.2. Chaos and limits to prediction 17 4.3. Quantifying predictability 19 5. About Entropy 22 5.1. Entropy and information 22 5.2. The Landauer principle 23 5.3. The entropy as a relative concept 24 5.4. Maxwell’s demon 26 5.5. The Gibbs paradox 28 5.6. The maximal entropy principle of Jaynes 29 5.7. Ockham’s razor 30 5.8. Coarse graining and irreversibility 31 5.9. Coarse graining and renormalization 33 5.10. Adding the entropy of subsystems 34 5.11. Beyond the Boltzmann, Gibbs and Shannon entropy: the Tsallis entropy 35 6. Quantum information 38 6.1. Quantum states and the definition of a qubit 39 6.2. Observables 42 6.3. Quantum evolution: the Schrödinger equation 42 6.4. Quantum measurements 43