8803-Information and Entropy (Fall 2015)

Morceaux Choisis
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   I- INFORMATION:     (back to "Information")
What is Information? Encoding, invariance.
Shannon Entropy.
Interpretations of Entropy: optimal encoding, channel capacity theorem.
Randomness, Markov Processes, Exit times, Equilibrium and non-equilibrium.

   II)- THERMODYNAMICS: a reminder     (back to "Thermodynamics")
concept of micro-state, probabilistic description, observables.
First Law: conservation laws. Energy, Noether's Theorem.
Thermodynamical Ensembles.
Second Law, Gibbs states, Lagrange multipliers and thermodynamical interpretation.
Out of Equilibrium: local equilibrium approximation. Currents.
Conservation laws and entropy production.
Linear response theory: transport coefficients, Onsager relations.
Strong irreversibility: the Gallavotti-Cohen Theorem

   III)- An example: BULK METALLIC GLASSES.     (back to "Bulk Metallic Glasses")
Physical properties, heat capacity, glass-liquid transition, viscosity, time scales.
Mechanical properties: strain-stress relation, elasticity, elasticity limit, plasticity.
Elasticity theory, phonons. Lifetime in liquid state. Insufficiency of elasticity theory.
Atomic scale Encoding: Delone sets, Voronoi tiling,
Delone graphs, acceptance domains.
Likelihood: genericity (topology) and almost sure properties (probability).
Anankeon Theory: the empty sphere property, jumps, contiguity graph.
Atomic stress. Description of the liquid phase. Law of Dulong-Petit.
Eshelby's theory. Liquid-glass temperature transition.
A Markov process: jump probability and waiting time. Viscosity.
Eshelby's renormalization and viscosity.
PDF: definition. Egami's oscillations. Spin-Glass model for equilibrium.

   IV)- PRODUCING INFORMATION     (back to "Producing Information")
Computers as thermal machines: Necessity of being out of equilibrium.
Erasing a bit (Landauer)
Life as an information production machine:
Krebs cycle, ATP-ADP ratio in cells, telomeres and death.
The food chain: from human to photosynthesis. From UV to IR radiation
Nuclear reactions in Earth, Sun and Stars, Stars evolution,
Gravity as a permanent source of instabilities.

   V)- COMPUTERS, ALGORITHMS, COMPLEXITY     (back to "Computers...")
Turing machines, algorithm. Stopping time.
Kolmogorov algorithmic complexity. Chaikin incompleteness Theorem.
Universal probability. The Occam razor. Relation with entropy.
Physics Laws as algorithm.
Von Neumann Computer Architecture
Self-replication: nanorobots (v. Neumann), example for molecules, DNA, proteins.
Statistical Mechanics of self-replication: the work of J. England
Libchaber experiments with thermal machines. Emergence of life on Earth.
Nicolelis' relativistic brain.

   VI)-INFORMATION IN HUMAN SCIENCES     (back to "Human Sciences)
Bureaucracy: a thermodynamical modeling. Time scales. Stability.
History: Kingdom of Quin, Chinese Empire, French system.
Examples in Economy: the capitalist machinery.
Fuel: human needs and demography. Exponential growth.
Mathus and agricultural growth.
The origins: Venice and Genoa. Italian city-states. The Arsenal, trading and banking.
Industrial Revolution: the role of steam machines
Information revolution: the role of computer in finance.
The Pareto Law and Econophyiscs

   VII)- FROM QUANTUM INFORMATION TO GRAVITY     (back to "From Quantum Information to gravity")
Encoding quantum information: the concept of qubit.
Quantum circuits and quantum algorithms. Teleportation. Fourier Transform
Shor's algorithm. Consequences for encryptions and security
Entanglement. EPR paradox and Bell's inequalities. Aspect's experiment.
Entanglement entropy. Examples for solvable spin systems.
Tensor models of entangled ground states. Excitations, topological excitations.
Hawking's radiation in Black holes, Entropy & Temperature of black holes.
Susskind-Hawking debate, holography, Polchinski firewall,
Susskind complexity for retrieval of informations in AdS black holes.
Brian Swingle proposal: information -> tensor states -> gravity.