entropy skill
Problem-solving strategies for entropy in information theory
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Install the entropy skill
A skill is a folder. Copy it into your agent's skills folder and the agent loads it when the task matches its description.
git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git /tmp/Continuous-Claude-v3 mkdir -p ~/.claude/skills cp -r /tmp/Continuous-Claude-v3/.claude/skills/math/information-theory/entropy ~/.claude/skills/entropy
available in every project
In the Claude apps, zip the folder and upload it from the Skills settings. The folder on GitHub
The instructions your agent would load
SKILL.md as published, without the frontmatter. Read it on GitHub
Entropy
When to Use
Use this skill when working on entropy problems in information theory.
Decision Tree
- Shannon Entropy
- H(X) = -sum p(x) log2 p(x)
- Maximum for uniform distribution: H_max = log2(n)
- Minimum = 0 for deterministic (one outcome certain)
- scipy.stats.entropy(p, base=2) for discrete
- Entropy Properties
- Non-negative: H(X) >= 0
- Concave in p
- Chain rule: H(X,Y) = H(X) + H(Y|X)
- z3solve.py prove "entropynonnegative"
- Joint and Conditional Entropy
- H(X,Y) = -sum sum p(x,y) log2 p(x,y)
- H(Y|X) = H(X,Y) - H(X)
- H(Y|X) <= H(Y) with equality iff independent
- Differential Entropy (Continuous)
- h(X) = -integral f(x) log f(x) dx
- Can be negative!
- Gaussian: h(X) = 0.5 log2(2piesigma^2)
- sympycompute.py integrate "-f(x)log(f(x))" --var x
- Maximum Entropy Principle
- Given constraints, max entropy distribution is least biased
- Uniform for no constraints
- Exponential for E[X] = mu constraint
- Gaussian for E[X], Var[X] constraints
Tool Commands
Scipy_Entropy
uv run python -c "from scipy.stats import entropy; p = [0.25, 0.25, 0.25, 0.25]; H = entropy(p, base=2); print('Entropy:', H, 'bits')"ScipyKlDiv
uv run python -c "from scipy.stats import entropy; p = [0.5, 0.5]; q = [0.9, 0.1]; kl = entropy(p, q); print('KL divergence:', kl)"Sympy_Entropy
uv run python -m runtime.harness scripts/sympy_compute.py simplify "-p*log(p, 2) - (1-p)*log(1-p, 2)"Key Techniques
From indexed textbooks:
- [Elements of Information Theory] Elements of Information Theory -- Thomas M Cover & Joy A Thomas -- 2_, Auflage, New York, NY, 2012 -- Wiley-Interscience -- 9780470303153 -- 2fcfe3e8a16b3aeefeaf9429fcf9a513 -- Anna’s Archive. What is the channel capacity of this channel? This is the multiple\-access channel solved by Liao and Ahlswede.
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
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