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Physics of Information: PHY 28A Winter 2025
Physics of Computation: PHY 28B Spring 2025

Announcements and Important Links:

Instructor: Professor Jim Crutchfield (Physics and Complexity Sciences Center)
Assistant: Jacob Hastings (Physics and Complexity Sciences Center)


Catalog numbers:
Winter 2025: Physics 256A Section 1 (CRN XXXXX)
Spring 2025: Physics 256B Section 1 (CRN XXXXX)

Level: Graduate
Units: 4

Online “flipped” course format:

Office Hours:
Crutchfield: W 0300-0400 PM, 197 Physics Bldg.
Hastings (TA): M 0130-0230 PM, 196 Physics Bldg or Zoom link or Meeting ID: 906 202 6165 and Passcode: 314.


The course explores how nature's structure reflects how nature computes. It introduces intrinsic unpredictability (deterministic chaos) and the emergence of structure (self-organization) in natural complex systems. Using statistical mechanics, information theory, and computation theory, the course develops a systematic framework for analyzing processes in terms of their causal architecture. This is determined by answering three questions: (i) How much historical information does a process store? (ii) How is that information stored? And (iii) how is the stored information used to produce future behavior? The answers to these questions tell one how a system intrinsically computes.

The course introduces tools to describe and quantify randomness and structure. It shows how they are necessarily complementary and how they are intimately related to concepts from the theory of computation. A number of example complex systems—taken from physics, chemistry, and biology—are used to illustrate the phenomena and methods. The course also takes time to reflect on the intellectual history of these topics, which is quite rich and touches on many basic questions in fundamental physics and the sciences and technology generally. New topics this year include complex materials and computation in quantum systems. The course will bring students to the research frontier in nonlinear physics and complex systems.

Flipped format: Watch lectures and work through interactive labs and homeworks online. Scheduled course time is allocated to hands-on problem solving, discussions on lectures, and introduction to online labs.

Physics of Information: Winter PHY 256A (Course Syllabus [PDF] [HTML])

Physics of Computation: Spring PHY 256B (Course Syllabus [PDF] [HTML])

Complex systems analyzed:

Audience: Graduate students in physics, mathematics, computer science, engineering, mathematical biology, and theoretical neuroscience. Others also welcome.

Prerequisites: Advanced undergraduate or introductory graduate differential equations, applied linear algebra, and probability theory. For example, at UC Davis these are covered in Mathematics 119A/B or 207A, 167 or 226A, and 135A/B or 235A, respectively; or in Physics 104A/B/C or 204A/B.

Reference materials:

  1. Lecture notes.
  2. Books:
  3. Computational Mechanics Reader.
  4. Supplemental Readings for historical background, projects, programming, and amusement.
  5. Software tools.

Course Work:

  1. Assigned Readings.
  2. Weekly Problem Sets (Both 256A and 256B, 40%).
  3. Mid-term Exam (PHY 256A Winter, 30%): Take home.
  4. Final Exam (PHY 256A Winter, 30%): Take home.
  5. Research Project (PHY 256B Spring, 60%):
    • Project report:
      • Orally presented as final exam during last class meetings.
      • Written report: Due electronically (TBA) June, end of day.
    • Project Presentation Schedule.
    • Report Organization.
    • Example projects can be found here.

All materials © James P. Crutchfield 2006-2025