Sethna - Entropy, Order Parameters and Complexity (9 Diapos)
Transcript of Sethna - Entropy, Order Parameters and Complexity (9 Diapos)
![Page 1: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/1.jpg)
Entropy, Order Parameters, and Complexity
Incorporating the last 50 years into the statistical mechanics curriculum
James P. Sethna, Cornell University, 2007http://www.physics.cornell.edu/sethna/StatMech/
The purview of science grows rapidly with time. It is the responsibility of each generation to join new insights to old wisdom, and to distill the key ideas for the next generation.
![Page 2: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/2.jpg)
Computation and EntropyBennett & Feynman’s Information Engine
Deep relation:Thermo Entropy: ΔS = Q/T
Info Entropy: S = -kB ∑ ρ log ρ
No minimum measurement energyInformation transformed into work
Minimalist magnetic tape
• Reversible computation• Entropy of glasses• Card shuffling & entropy
Extract kBT from each bit if atom position known: information into work!
![Page 3: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/3.jpg)
Computational ComplexityStatistical mechanics of NP-complete problems
NP-complete problems• Traveling salesman• 3-colorability• Number partitioning• Logical satisfiability (SAT)• Worst case: exponential time
Random instances may not be hard…Ensembles; statistical mechanics; phase transitions; spin glass methods…
![Page 4: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/4.jpg)
Dynamical SystemsChaos, Ergodicity, and KAM
Why equilibrium?Chaos destroys initial stateErgodicity
Why has the earth not left the solar system (equilibrium)?• KAM theorem: invariant tori• Breakdown of ergodicity
![Page 5: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/5.jpg)
Social SciencesEconophysics, social networks
Stock prices and random walks• Volatility, diversification• Heavy tails• Derivatives, Black-Scholes …
Six degrees of separation• Small world networks• Betweenness algorithms
Watts and Strogatz
![Page 6: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/6.jpg)
Biology(Chris Myers, Michelle Wang)
Random walks; Ratchet and pawl; ‘Force’ free energy
Molecular motors
Ion pump as Maxwell’s demon
Na+Na+
Na+
K+K+
K+ Genetic Networks• Stochastic evolution• Monte Carlo• Shot noise• Telegraph noise
ProteinmRNAregulator
Elowitz and Leibler
![Page 7: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/7.jpg)
Growth and evolutionPatterns and correlations
Microwave background• Wave equations• Correlation functions
Snowflakes and dendrites
• Growth dynamics• Linear stability
Martensites• Non-convexity• Microstructure
![Page 8: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/8.jpg)
Complexity, scalingand the Renormalization Group
Scale invariance
Fractal Structures
Universality
![Page 9: Sethna - Entropy, Order Parameters and Complexity (9 Diapos)](https://reader030.fdocuments.us/reader030/viewer/2022020223/577cc7bc1a28aba711a1b18a/html5/thumbnails/9.jpg)
Entropy, Order Parameters, and Complexity
Incorporating the last 50 years into the statistical mechanics curriculum
Statistical mechanics is important to students and researchers in mathematics, biology, engineering, computer science and the social sciences. It will be taught in all of these fields of science in the next generation, either in physics departments or piecemeal in each field. By teaching statistical mechanics to a variety of fields, we enrich the subject for those with backgrounds in physics.