entropy
Calculate Shannon entropy, KL divergence, and other information theory metrics.
Install
mkdir -p .claude/skills/entropy && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/4596" && unzip -o skill.zip -d .claude/skills/entropy && rm skill.zipInstalls to .claude/skills/entropy
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for entropy in information theoryKey capabilities
- →Calculate Shannon entropy
- →Compute KL divergence
- →Solve differential entropy equations
- →Perform entropy property proofs
How it works
Interface for Scipy and Sympy to execute information theory math scripts based on defined axioms.
Inputs & outputs
When to use entropy
- →Calculating Shannon entropy for datasets
- →Computing KL divergence between distributions
- →Solving differential entropy equations
About this skill
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)
z3_solve.py prove "entropy_nonnegative"
-
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(2pie*sigma^2)
sympy_compute.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')"
Scipy_Kl_Div
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.
When not to use it
- →Simple data compression tasks
- →Non-information theory math
Prerequisites
Limitations
- →Requires mathematical setup
- →Cannot prove human intent
How it compares
It automates the application of theoretical information formulas to concrete computational inputs.
Compared to similar skills
entropy side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| entropy (this skill) | 2 | 7mo | Review | Advanced |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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