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

Announcements and Important Links:

• Roadmap: Access to Lectures, Readings, and Homeworks. Updated weekly.
• CMPy Cloud: Access online interactive notebooks (Labs and Homeworks).
• Subscribe/unsubscribe for course announcements on list poci-w3. Enrolled students automatically added.
• Awarded First Prize in Teaching Dynamical Systems by the Society for Industrial and Applied Mathematics.

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

WWW: csc.ucdavis.edu/~chaos/courses/poci/

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:

• In-Person Class meetings: Tuesday, Thursday 1210-0130 PM, 185 Physics Building.
  
• Online:
  Lectures: Watch videos at Roadmap.
  Interactive labs via CMPy Cloud.
  

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.

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

• Weeks 1-4: Self-Organization—Nonlinear dynamics and pattern formation
• Weeks 5-6: Measurement Theory—Symbolic dynamics and stochastic processes)
• Weeks 7-10: Information Processing—Information theory for complex, correlated processes

• Weeks 1-4: Intrinsic Computation—Computational mechanics
• Weeks 6-8: Applications—Complex Materials, Quantum Dynamics, Information Thermodynamics
• Weeks 9-10: Projects

Complex systems analyzed:

• Low-dimensional chaos and routes to chaos
• Complex stochastic processes and hidden Markov models
• Cellular automata
• Spin systems and networks
• Structured-disordered one-dimensional materials
• Quantum dynamical systems
• Thermodynamic Computing: Maxwellian demons and information engines

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:
   • Elements of Information Theory, T. M. Cover and J. A. Thomas, Second Edition, Wiley-Interscience, New York (2006).
   • Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering, S. H. Strogatz, Second Edition, Addison-Wesley, Reading, Massachusetts (2014).
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