Statistical Mechanics of Computing Systems

Photo credit: https://www.flickr.com/photos/constructor_trurl/4250128996

This is a workshop hosted collaboratively by
*Lingfei Wu ** (Knowledge Lab, Computation Institute, University of Chicago),
Lei Ma * (Department of Physics and Astronomy, University of New Mexico) ,
**Qian-Yuan Tang ** (School of Physics, Nanjing University ), and
**Yanbo Zhang ** (School of Physical Sciences, University of Science and Technology of China).

Questions to be considered:

1. Why can we ignore the causality between microstates in studying the equilibrium states (at the macro-level) of particle systems ? Are there similar situations in computing systems ? Can we apply ergodic assumption and the maximum entropy principle in computing systems ?

2. Can we define "energy" in computing systems, such as cellular automata and tag systems ? Can we use Boltzman function to describe the relationship between "energy" and "probability" in the ensemble of computing systems ?

3. Does rule 110 (following Wolfram's tradition), which is proved to be Turing complete among all the 256 rules, different from other cellular automata in statistical properties ? Do universal Turing machines always show statistical properties different from non-universal machines in various computing systems ?

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I. Review of Statistical Mechanics

by Lei Ma

• Review 1
• Review 2
• Review 3
  References
  Ma's note for stat-mech course
  Reichl, L. E., & Prigogine, I. (1980). A modern course in statistical physics(Vol. 71). Austin: University of Texas press.

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II. Computing Systems

by Lingfei Wu

• Turing Machine
• Tag System
• Lambda calculus
• Cellular Automata I
• Cellular Automata II
  References
  Turing, A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. J. of Math, 58(345-363), 5.
  Church, A. (1940). A formulation of the simple theory of types. The journal of symbolic logic, 5(02), 56-68.
  Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of modern physics, 55(3), 601.
  Cook, M. (2004). Universality in elementary cellular automata. Complex Systems, 15(1), 1-40.

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III. Patterns

• Networked systems: species, cities, and websites
  (Scale-free network model and geometric random graph model)
  *by Lingfei Wu *
  References
  Barabási, A. L., & Albert, R. (1999). Emergence of scaling in random networks.science, 286(5439), 509-512.
  Zhang, J., Li, X., Wang, X., Wang, W. X., & Wu, L. (2015). Scaling behaviours in the growth of networked systems and their geometric origins. Scientific reports, 5.
• Programming languages and softwares
  by Yanbo Zhang

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IV. Intelligence

• Boltzman Machine
  *by Lingfei Wu *
• Causal entropic forces
  by Qian-yuan Tang
  References
  Wissner-Gross, A. D., & Freer, C. E. (2013). Causal entropic forces. Physical review letters, 110(16), 168702.