[Leejohnston]

## Entropy & Information — Why Order Has a Cost

### 1. The Equation

Entropy:

S = k ln W

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### 2. What Each Symbol Means

- S = entropy
- k = Boltzmann constant
- W = number of microstates

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### 3. What the Equation Is Telling Us

Entropy measures **how many ways a system can be arranged internally**.

More microstates → higher entropy.

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### 4. Where It Comes From (Intuition)

Order is rare. Disorder is common.

Systems naturally drift toward the most probable state.

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### 5. Why This Matters

Entropy links:
- thermodynamics
- information theory
- time’s arrow
- black holes

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### 6. Real-World Applications

- Computing
- Heat engines
- Cosmology
- Information theory

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### 7. Common Misconceptions

- Entropy means mess → misleading
- Entropy forbids life → false
- Entropy is subjective → false

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### Try It Yourself

Why does deleting information always generate heat?