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Entropy & Information — Why Order Has a Cost - Leejohnston - 01-08-2026
## 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?