Preliminary Step

Before starting the project, convert the course notebooks into standalone Python scripts. This is a necessary step for running experiments on the cluster, where Jupyter is impractical and batch submissions require executable .py files.

Convert the following notebooks into standalone .py scripts:

• 06_full_agent.py:the complete single-agent Physics Research Assistant
• 08_multi_agent_team.py: the 3-agent sequential CrewAI team
• 09_debate_agent.py:the 3-agent Debate crew

Goal

Treat LLM agents as particles in a statistical mechanics system. Study how consensus emerges (or fails to emerge) in a population of agents as a function of temperature and interaction structure. Produce quantitative measurements and discuss the analogy with thermodynamic phase transitions.

Part 1 - Single-Agent Temperature Sweep

Use the naked LLM (the chat() function from Module 1.0, with no tools) to study how the LLM's output distribution depends on temperature.

The question (fixed for all runs):

"The critical temperature of the 2D Ising model is T_c = 2.269 and Euler's number is e = 2.718. Compute the ratio T_c / e. Give only a numerical value, without explanation."

This question is deliberately simple arithmetic, but the specific ratio T_c / e ≈ 0.8347 is certainly not memorized by any model. Both constants are well-known, so any variance in the output comes purely from the computation step, not from knowledge uncertainty. This isolates the effect of temperature on the model's "reasoning noise."

Protocol:

• Run this question 30 times at each of 7 temperatures: T ∈ {0.1, 0.3, 0.5, 0.7, 1.0, 1.5, 2.0}
• Extract the numerical value from each response (write a parser that handles variations like "0.8347", "approximately 0.835", "≈ 0.83", etc.)
• Discard responses where no number can be extracted (record the discard rate)

Measurements at each temperature:

• Mean and standard deviation of the extracted estimates
• Histogram of the estimates (with 20 bins spanning 0.5–1.2)